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In this paper we consider new geometric flow equations, called D-flow, which describe the variation of space-time geometries under the change of the number of dimensions. The D-flow is originating from the non-trivial dependence of the volume of space-time manifolds on the number of space-time dimensions and it is driven by certain curvature invariants. We will work out specific examples of D-flow equations and their solutions for the case of D-dimensional spheres and Freund-Rubin Compactification. The discussion of the paper is motivated from recent swampland considerations, where the number $D$ of space-time dimensions is treated as a new swampland parameter., Comment: 30 pages, 6 figures

This paper illustrates various aspects of the ER=EPR conjecture. It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges. The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern. The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$ supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the $\mathcal{N}=2$ supergravities we are able to make a general statement on the possible $\alpha$-attractor models which can obtained upon truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical constraints restrict the allowed values of the parameter $\alpha$ to be $\alpha=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in particular on the so called $c$-map connection between Quaternionic K\"ahler manifolds starting from Special K\"ahler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self-contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of $\mathcal{N}=2$ supergravities is reviewed in some detail.

Following an outline of the Large Hadron Collider, this paper will analyze CERN's scientific plans for high-energy colliders for the years to come. The immediate plans include the upgrades to the Large Hadron Collider and its injectors. This may be followed by a linear electron-positron collider, the Compact Linear Collider. This paper describes the design of these future colliders at CERN, all of which have a unique value to add to experimental particle physics

In this paper we briefly review the main results obtained in arXiv:0812.1982, where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincare' algebra in 4 dimensions with two central charges. We derive all independent Casimir operators of VSUSY and we find two distinct spin-related operators in the case of nonvanishing central charges. One is the analogue of superspin for VSUSY and the other is a new spin, called C-spin, whose value is fixed to 1/2. We also show that the VSUSY algebra and its Casimir operators can be derived by an Inonu-Wigner contraction from OSp(3,2|2). This paper is based on the talk given in Varna, Bulgaria, during the 4-th EU RTN Workshop 2008.

Quantum Turing machines are discussed and reviewed in this paper. Most of the paper is concerned with processes defined by a step operator $T$ that is used to construct a Hamiltonian $H$ according to Feynman's prescription. Differences between these models and the models of Deutsch are discussed and reviewed. It is emphasized that the models with $H$ constructed from $T$ include fully quantum mechanical processes that take computation basis states into linear superpositions of these states. The requirement that $T$ be distinct path generating is reviewed. The advantage of this requirement is that Schr\"{o}dinger evolution under $H$ is one dimensional along distinct finite or infinite paths of nonoverlapping states in some basis $B_{T}$. It is emphasized that $B_{T}$ can be arbitrarily complex with extreme entanglements between states of component systems. The new aspect of quantum Turing machines introduced here is the emphasis on the structure of graphs obtained when the states in the $B_{T}$ paths are expanded as linear superpositions of states in a reference basis such as the computation basis $B_{C}$. Examples are discussed that illustrate the main points of the paper. For one example the graph structures of the paths in $B_{T}$ expanded as states in $B_{C}$ include finite stage binary trees and concatenated finite stage binary trees with or without terminal infinite binary trees. Other examples are discussed in which the graph structures correspond to interferometers and iterations of interferometers., Comment: 21 pagaes Latex plus 5 postscript figures, submitted to Fortschritte der Physik

This paper studies the structural formation of various spherically symmetric anisotropic configured stars in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity under the influence of electromagnetic field, where $\mathcal{Q}=\mathcal{R}_{\eta\sigma}\mathcal{T}^{\eta\sigma}$. We construct modified field equations by adopting the Krori-Barua metric potentials (involving unknowns ($A,B,C$)) and employ bag model equation of state to explore the physical characteristics of compact structures like Vela X-I,~4U 1820-30,~SAX J 1808.4-3658,~Her X-I and RXJ 1856-37. The bag constant ($\mathfrak{B_c}$) and other three unknowns are calculated by using experimental data of all considered stars. Further, we adopt a standard model $\mathcal{R}+\varpi\mathcal{R}_{\eta\sigma}\mathcal{T}^{\eta\sigma}$ to interpret the graphical behavior of energy density, pressure in radial and tangential directions as well as anisotropy. We also investigate mass, compactness parameter, surface redshift and energy conditions for compact bodies by taking model parameter ($\varpi$) as $\pm5$. The stability of the obtained solution is examined by means of two different criteria. We conclude that our proposed solution meets all the physical requirements and shows stable behavior everywhere for $\varpi=5$., Comment: 39 pages, 8 figures

In this work, we explored the effect of the fuzzy dark matter (FDM) (or wave dark matter) halo on a supermassive black hole (SMBH). Such a dark matter introduces a soliton core density profile, and we treat it ideally as a spherical distribution that surrounds the SMBH located at its center. In this direction, we obtained a new metric due to the union of the black hole and dark matter spacetime geometries. We applied the solution to the two known SMBH - Sgr. A* and M87* and used the empirical data for the shadow diameter by EHT to constrain the soliton core radius $r_\text{c}$ given some values of the boson mass $m_\text{b}$. Then, we examine the behavior of the shadow radius based on such constraints and relative to a static observer. We found that different shadow sizes are perceived at regions $r_\text{obs}r_\text{c}$, and the deviation is greater for values $m_\text{b}, Comment: 19 pages, 9 figures, 2 tables. Finalized version of the paper

In even spacetime dimensions, the interacting bosonic conformal higher-spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model $\mathcal{S}[\varphi,h]$ describing a complex scalar field $\varphi$ coupled to an infinite set of background CHS fields $h$, with $\mathcal{S}[\varphi,h]$ possessing a non-abelian gauge symmetry. Two characteristic features of the perturbative constructions of $\mathcal{S}[\varphi , h]$ given in the literature are: (i) the background spacetime is flat; and (ii) conformal invariance is not manifest. In the present paper we provide a new derivation of this action in four dimensions such that (i) $\mathcal{S}[\varphi , h]$ is defined on an arbitrary conformally-flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the $\mathcal{N}=1$ supersymmetric case. Specifically, we construct, for the first time, a model $\mathcal{S}[\Phi, H]$ for a conformal scalar/chiral multiplet $\Phi$ coupled to an infinite set of background higher-spin superfields $H$. Our action possesses a non-abelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal half-integer superspin multiplets. The other fundamental features of this model are: (i) $\mathcal{S}[\Phi, H]$ is defined on an arbitrary conformally-flat superspace background; and (ii) the background $\mathcal{N}=1$ superconformal symmetry is manifest. Making use of $\mathcal{S}[\Phi, H]$, an interacting superconformal higher-spin theory can be defined as an induced action., Comment: 69 pages; V2: References and new comments added, typos corrected; V3: Published version

In this paper I will further investigate the spectrum of quantum gravity or string theories at large number of dimensions. We will see that volumes of certain orbifolds shrink at large D. It follows that the mass spectra of the leading Kaluza-Klein towers and also of wrapped brane states on these orbifolds possess a non-trivial dependence on D: KK modes become heavy at large D, whereas wrapped branes become light. This observation can be used either to apply the Large Dimension Conjecture or, as we will do, to investigate the possibility of a D-duality symmetry, which relates in gravity compactifications of different dimensions. We will set up the general rules for D-duality in higher dimensional gravity. However due to existence of the critical dimensions, D-duality is quite restricted in string theory. As simple tests for D-duality in string theory, we will discuss the duality between M-theory on a two-dimensional orbifold, namely the M\"obius strip, and an IIB S-fold on a circle, which corresponds to the heterotic CHL string, as well the duality between a (truncated) 12-dimensional theory on a three-dimensional orbifold and another IIB S-fold compactification. Finally I also comment on the possible existence of exotic theories at large D., Comment: 36 pages, revised version contains only small changes

The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of foliated field theories which, roughly, are built by coupling together fields supported on the leaves of foliations of spacetime. Another approach, which we refer to as exotic field theory, focuses on constructing Lagrangians consistent with special symmetries (like subsystem symmetries) that are adjacent to fracton physics. A third framework is that of infinite-component Chern-Simons theories, which attempts to generalize the role of conventional Chern-Simons theory in describing (2+1)D Abelian topological order to fractonic order in (3+1)D. The study of these theories is ongoing, and many of their properties remain to be understood. Historically, it has been fruitful to study QFTs by embedding them into string theory. One way this can be done is via D-branes, extended objects whose dynamics can, at low energies, be described in terms of conventional quantum field theory. QFTs that can be realized in this way can then be analyzed using the rich mathematical and physical structure of string theory. In this paper, we show that foliated field theories, exotic field theories, and infinite-component Chern-Simons theories can all be realized on the world-volumes of branes. We hope that these constructions will ultimately yield valuable insights into the physics of these interesting field theories., Comment: 40 pages. 8 figures. 8 tables. Corrected typos. Modified references and acknowledgements. Adjusted formatting

In this paper, we have presented the big rip and pseudo rip cosmological models in an extended theory of gravity. The matter field is considered to be that of perfect fluid. The geometrical parameters are adjusted in such a manner that it matches the prescriptions given by cosmological observations, to be specific to the range of Hubble tension $(H_{0})$. The models favor phantom behavior. The violation of strong energy conditions are shown in both the models, as it has become essential in an extended gravity. The representative values of the coupling parameter are significant on the evolution of the universe., 14 pages, 18 figures

In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a curved background. The non-commutative geometry is given by an infinite-dimensional Bott-Dirac type operator, whose square gives the Hamilton operator, and which interacts with an algebra generated by holonomy-diffeomorphisms. The Bott-Dirac operator and the associated Hilbert space relies on a metric on the configuration space of connections, which effectively works as a covariant ultra-violet regulator. We show that the construction coincides with perturbative quantum field theory in a local limit. Questions concerning Lorentz invariance and the fermionic sector are left open.

In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0_S-resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras. This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras. We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature.

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrodinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large-scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set-up might provide an interesting new arena for testing the ideas of holography and gravitational duals.

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kahler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either Z(2) or contain Z(4), Z(2) x Z(2), Z(3) or Z(5) as a subgroup. The Hodge numbers for the quotients for which the group G contains Z(3) or Z(5) have been computed previously. This paper deals with the remaining cases, for which G superset of Z(4) or G superset of Z(2) x Z(2). We also compute the Hodge numbers for 99 of the 166 CICY's which have Z(2) quotients.

In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.

In this paper we review the appearance and utility of a nilpotent chiral multiplet in the context of supergravity, string theory and cosmology. Coupling a nilpotent chiral superfield to supergravity, one obtains what is called pure dS supergravity, a supergravity theory without scalar degrees of freedom that naturally has de Sitter (dS) solutions, and in which supersymmetry is non-linearly realized. We extend previous results that couple this dS supergravity to chiral and vector multiplets and derive the most general supergravity action for a single nilpotent chiral multiplet coupled to supergravity and an arbitrary number of chiral and vector multiplets.

Soft behaviour of closed string amplitudes involving dilatons, gravitons and anti-symmetric tensors, is studied in the framework of bosonic string theory. The leading double soft limit of gluons is analysed as well, starting from scattering amplitudes computed in the open bosonic string. Field theory expressions are then obtained by sending the string tension to infinity. The presented results have been derived in the papers of Ref.[1].

We consider in the paper the Nonsymmetric Kaluza–Klein Theory finding a condition for a color confinement in the theory. We consider also a Kerner–Wong–Kopczynski equation in this theory. The Nonsymmetric Kaluza–Klein Theory with a spontaneous symmetry breaking and Higgs' mechanism is examined. We find a mass spectrum for a broken gauge bosons and Higgs' particles. We derive a generalization of Kerner–Wong–Kopczynski equation in the presence of Higgs' field. A new term in the equation is a generalization of a Lorentz force term for a Higgs' field. We consider also a bosonic part of GSW (Glashow–Salam–Weinberg) model in our theory, getting masses for W, Z bosons and for a Higgs' boson agreed with an experiment. We consider Kerner–Wong–Kopczynski equation in GSW model obtaining some additional charges coupled to Higgs' field.

In this paper we argue that a firewall is simply a manifestation of an inconsistent truncation of non-perturbative effects that unitarize the semiclassical black hole. Namely, we show that a naive truncation of quantum corrections to the Hawking spectrum at order O(e(-S)), inexorably leads to a "localised" divergent energy density near the black hole horizon. Nevertheless, in the same approximation, a distant observer only sees a discretised spectrum and concludes that unitarity is achieved by O(e(-S)) effects. This is due to the fact that instead, the correct quantum corrections to the Hawking spectrum go like O(g(tt)e(-S)). Therefore, while at a distance far away from the horizon, where g(tt) approximate to 1, quantum corrections are perturbative, they do diverge close to the horizon, where g(tt) -> infinity. Nevertheless, these "corrections" nicely re-sum so that correlations functions are smooth at the would-be black hole horizon. Thus, we conclude that the appearance of firewalls is just a signal of the breaking of the semiclassical approximation at the Page time, even for large black holes.

The Nonsymmetric Kaluza–Klein (Jordan–Thiry) Theory leads to a model of a modified acceleration that can fit an anomalous acceleration experienced by the Pioneer 10 and 11 spacecraft. The future positions of those spacecrafts are predicted using distorted hyperbolic orbit. A connection between an anomalous acceleration and a Hubble constant is solved in the theory together with a relation to a cosmological constant in CDMΛ model. In the paper we consider an exact solution of a point mass motion in the Solar System under an influence of an anomalous acceleration. We find two types of orbits: periodic and chaotic. Both orbits are bounded. This means there is no possibility to escape from the Solar System. Some possibilities to avoid this conclusion are considered. We resolve also a coincidence between an anomalous acceleration and the cosmological constant using a paradigm of modern cosmology. Relativistic effects and a cosmological drifting of a gravitational constant are considered. The model of an anomalous acceleration does not cause any contradiction with Solar System observations. We give a full statistical analysis of the model. We consider also a full formalism of the Nonsymmetric Jordan–Thiry Theory for the problem and present a relativistic model of an anomalous acceleration. We consider the model for General Relativity approximation, i.e. (). In this model there are no contradictions with General Relativity tests in the Solar System. Pioneer 10/11 spacecrafts will come back in 106 years (a time scale of our periodic solutions is 106 years). Moreover, almost relativistic or relativistic spacecrafts can escape from the Solar System. We consider also a model of a relativistic acceleration which is more complicated, with taken into account.

Complexity in quantum physics measures how difficult a state can be reached from a reference state and more precisely it is the number of fundamental unitary gates we have to operate to transform the reference state to the state we are considering. In the holographic context, based on several explicit calculations and arguments, it is conjectured that certain bulk volume calculates the boundary field theory subregion complexity. In this paper, we will show that the deformation shows a strong signal of the correctness of this complexity equals volume conjecture. A bonus is a way to look at the deformation, by its reversibility, as operating a unitary quantum circuit which prepares states in quantum field theory.

In the paper the perturbation theory is constructed for QED, for which the interaction with the external pair-creating field is kept exactly. An explicit expression for the perturbation theory causal electron propagator is found. Special features of usage of the unitarity conditions for calculating the total probabilities of radiative processes in the case are discussed. Exact Green functions are introduced and the functional formulation is discussed. Perturbation theory for calculating the mean values of the Heisenberg operators, in particular, of the mean electromagnetic field is built in the case under consideration. Effective Lagrangian which generates the exact equation for the mean electromagnetic field is introduced. Functional representations for the generating functionals introduced in the paper are discussed.

The paper summarizing the recent results of the author is devoted to a detailed analysis of positive semigroups appearing in dynamical description of non-equilibrium statistical mechanics. The first part of paper has a review character (this goes especially to sections 1 and 2). Novel aspects are contained in sections 3, 4 and 5. Section 4 contains the formulation and relatively complete discussion of detailed balance condition. In particular, the representation theorem for dynamical semigroups satisfying detailed balance is given. Section 5 contains new results from the theory of strongly and strictly positive semigroups.

The aim of these two papers (I and II) is to try to give a unified systematic description of the different quantum mechanical realization of the unitary representations of the inhomogeneous space-time groups. Paper I, which is more general, deals with the interrelationships between the Mackey, the Wigner and the covariant realizations of induced representations, first for general groups, and then for semi-direct products. The Euclidean, Galilean and Poincare groups are treated in some detail as examples. Paper II gives a systematic treatment of the various covariant wavefunctions (Dirac, Bargmann-Wigner, etc.) that can be used to describe a single irreducible representation of the Poincare group. It is self-contained and deals first with momentum space, and then with first and second quantized fields. In both papers the treatment is index-free.

As shown in previous papers, Reggeon “Field” Theory is actually a Markov process describing the evolution of wee partons during a boost. In the present paper, the physical interpretation of scattering amplitudes and cross sections is discussed, both for the uncut (unlabelled) and cut (labelled) version. Elastic amplitudes and total cross sections, inclusive cross sections, fully diffractive events, and inelastic diffraction are all shown to have simple interpretations in the parton model. Finally, the connection with models for evolution of hard partons in QCD is discussed.

The aim of Part I1 of this paper is to try to give a unified, systematic description of the different covariant wave-functions (Dirac, Fierz, Bargmann-Wigner etc.) which can be used to carry the same physical representation of the Poincark group. The procedure is based on the observation that the most important physical properties of the wave-functions, in particular the transformation law, the wave-equation, and the inner-product, depend only on the representation of the Lorentz group to which the wave-functions belong and the spin-projection. Accordingly, a formalism is set up which is valid for all (finite-dimensional) representations of the Lorentz group and all spin projections and so allows all the various wave-equations which are possible for a given mass and spin to be discussed collectively. The formalism is relatively simple and transparent (possibly even more simple and transparent than any of the special rases it embraces) and it allows the various conventional wave-functions and wave-equations to be easily identified as special cases. The topics covered in the discussion are listed in the table of contents, and Part 11 of the paper has been made self-contained so that it can be read independently of Part I.

In the present paper it is shown that the Born diagram model with an overall phenomenological form factor suggested in papers [2, 3] on the basis of the ideas of universal interaction of Q-meson with hadrons describes well the experimental data on the reaction π−p Q°n in a wide range of energies 2.7 GeV/c ≦ QL ≦ 17 GeV/c at small momentum transfers |t| ≦ 0.2 (GeV/c)2. The connection of the Born diagram model with the other high energy models is considered. On one hand, we show that the absorption account in many respects, though not literally, comes to forming an overall form factor. On the other hand, the normalization of amplitudes of the traditional absorptive one-pion exchange models to the Born diagrams at t = 0 lays on the absorptive parameters the condition σtotC/8πA = 1 corresponding to the total absorption of the low partial waves. In this case the one-pion exchange models with absorption coincide at all t with the Born diagram model with absorption and the reaction aplitudes are independent of a choice of the initial vector theory Lagrangian.

The paper, summarizing the results of recent papers of the author, is devoted to a detailed analysis of postulates of nonrelativistic quantum theory appearing within two classical axiomatic frameworks the “quantum logic” and the “algebraic approach” respectively, which are presently the two main alternatives for quantum axiomatics. The first part of the paper concerns the structure of two important sets, the set of questions (propositional logic) and the set of pure states. It is shown how the quantum logic axiomatic scheme can be modified and improved in order to overcome the well known troubles connected with the lack of satisfactory physical justification for some postulates of this approach. In particular, an axiom system is developed, related closely to the quantum logic axiomatic scheme, in which the questions of the complete lattice structure, the atomisticity, and the validity of the covering law in the propositional logic do not appear so problematic. The particular attention is directed to the covering law, which is here obtained as a consequence of physically clear properties of the experimental procedures (“filters”) associated with the quantum-mechanical propositions. In Section 1.5 we formulate an axiom system for quantum mechanics based exclusively on the concepts of pure state, transition probability, and pure filter. In the second part of the paper the axiomatic scheme presented in Part 1 is developed with the aim to analyse the algebraic structure of some subspaces of the set of simple observables. The quantum logic axiomatic framework is here shown closely connected with the Jordan-Banach algebraic scheme. In the third part of the paper, similarly as it was done in Parts 1 and 2, the correspondence between the propositions and the experimental (measuring) procedures verifying these propositions is put as the basic assumption of the axiomatization of quantum mechanics. As a consequence of this assumption, there is established the structure of a real Jordan-Banach algebra in the set Ob of the bounded observables associated with a physical system, so that we can apply the GNS representation theorem proved recently for such algebras by Alfsen et al. (1978) to obtain the Hilbert space (or, to be more precise, the C*-algebraic) representation for Ob.

We give in this paper a detailed and unified description of the procedures which must be followed for all cases of physical interest to go from the wave functions carrying an irreducible representation of the restricted Poincare group, to objects having a manifestly covariant behaviour. As well known, for instance for the case of spin 1/2 massive particles, this amounts to performing the inverse of a Foldy-Wouthuysen transformation. Before coming to the main subject of the paper, the construction of the irreducible representations of the restricted and extended Poincare group are reviewed. Particular emphasis is given to the physical meaning of the representations and of the invariants which characterize them. After this, we derive manifestly covariant quantities from the wave functions of the irreducible representations of the restricted group for spin 0. 1/2 and 1, massive and massless elementary systems. The corresponding relativistically invariant equations, i.e. the Klein-Gordon, Dirac, Proca, Weyl and Maxwell equations are then derived. The transformations properties under the transformations of the extended group are also extensively discussed.

A number of experimental and theoretical papers have been devoted to the investigation of the electric and magnetic polarizabilities of nucleons. In the present paper, the results of these works are considered in detail. Theoretical and experimental data indicate that the geometrical dimensions of the pion seem to be of the same order as those of the nucleon, which would seem to indicate that the pion would be polarized under the influence of an electromagnetic field. This point is discussed in detail. (J.S.R.)

The paper demonstrates that negative ions formed by electrons drifting through a gas may commonly not be considered as being stable, but electron detachment must be taken into account. This is concluded investigating electron current pulses of avalanches which exhibit strong currents of „delayed” (i.e. detached) electrons in oxygen and air, but not in hydrogen, nitrogen and certain other electropositive gases. It is shown that this assumption allows to explain the observed current pulse shapes. An attachment coefficient η as function of E/p (= ratio of fieldstrength to pressure) is determined which arises from the dissociative attachment process, e + O2 O− + O. A detachment frequency 1/τ versus E/p is obtained which arsies from de-ionizing collisions of the same ion O−, which has been sufficiently energized by the electric field, O− + O2 e + O + O2, thus completing the evidence for the above conclusion. (In air a N2 molecule may act as well as O2 as colliding particle.) In addition, values of the electron ionization coefficient α/p and of the electron drift velocity v− are determined in oxygen (35 < E/p < 120 Volt/cm · Torr) and air (35 < E/p < 80). – The “electrical method” has been used. The initial photo electron pulse was released by the light of a high intensity spark of 5 · 10−9 s radiation pulse duration; the luminous tail has been suppressed by a Kerr cell shutter. In the first section of the following paper the theoretical analysis is given in a generalized form and a number of electron delaying processes are discussed, such as the Penning and Hornbeck effects and auto-deionization of negative ions. The second section describes the experiments and the interpretation of the results. In the third section an attempt is made to discuss the observations of other authors on the subject with respect to electron detaching collisions. The present results are significant for explaining some discrepancies in the determination of electron attachment coefficients in oxygen and air, in which de-ionization has hitherto not been taken in account.

Starting from a recent paper [13] we derive a new representation of the left-hand cut contribution for the πN system. This representation makes it possible to calculate the generalized πN potential accurately from phase shifts and high energy models, because it contains only the imaginary parts of the partial wave amplitudes in the physical region. The analytic properties, the region of convergence and the physical content of this representation is discussed. We propose to use this left-hand cut contribution in bootstrap calculations, because it is more reliable than the approximate expressions which have been used in previous papers. – The left-hand cut contributions are calculated and compared with the nucleon and Δ (1236) approximation for the ƒ, ƒ, ƒ and ƒ partial wave amplitudes.

The propagation of thermal and mechanical disturbances in a non-conducting crystal is studied on the basis of a generalized transport equation for phonons, derived in a previous paper. This equation agrees with the Peierls-Boltzmann equation for slowly varying inhomogeneities in space and time and is consistent with the perturbation treatment of the phonon self energy for high frequencies and short wave-lengths. A formal solution of the transport equation is obtained, which allows us to study in detail the transition between the low-frequency, collision-dominated regime and the high-frequency, essentially collision-less regime. Using a single relaxation time approximation we discuss the propagation of “sound” waves and obtain explicit expressions for the dispersion of the sound velocity and the damping, valid for arbitrary frequencies. In order to elucidate more clearly the technique used we consider in this paper an one-dimensional crystal, but the essential results can easily be taken over to the threedimensional case. A separate report on this will be published elsewhere.

It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.

There have been recent advances in the construction of algebraic curves for certain classes of string solutions in the context of the AdS/CFT correspondence. In this paper we obtain the Lax operators and associated spectral curves for circular and folded string solutions in AdS. In addition, we provide an original approach for the reconstruction of string solutions in S3 from their corresponding curves.

Four-Dimensionally Regularized/Renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet counterterms. In this paper I prove that integration-by-parts (IBP) identities based on simple integrand differentiation can be used to find relations among multi-loop FDR integrals. Since algorithms based on IBP are widely applied beyond one loop, this result represents a decisive step forward towards the use of the FDR approach in multi-loop calculations.

Type II theories can be described as the endpoint of closed string tachyon condensation in certain orbifolds of supercritical type 0 theories. In this paper, we study solitons of this closed string tachyon and analyze the nature of the resulting defects in critical type II theories. The solitons are classified by the real K-theory groups KO of bundles associated to pairs of supercritical dimensions. For real codimension 4 and 8, corresponding to $KO({\bf S}^4)={\bf Z}$ and $KO({\bf S}^8)={\bf Z}$, the defects correspond to a gravitational instanton and a fundamental string, respectively. We apply these ideas to reinterpret the worldsheet GLSM, regarded as a supercritical theory on the ambient toric space with closed tachyon condensation onto the CY hypersurface, and use it to describe charged solitons under discrete isometries. We also suggest the possible applications of supercritical strings to the physical interpretation of the matrix factorization description of F-theory on singular spaces.

We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two-brane solutions where Arnold-Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the operator on a three-torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups Γ.

In this paper we consider the -graded parity generalizing the ordinary (or Z2-graded ) parity. Using the -graded parity operator, we discuss the minimal bosonization of the N=2 SUSY with -graded parity. The lowest energy level is shown to be infinitely degenerate. In order to avoid the infinite degeneracy of the ground state we introduce the paraboson algebra to obtain the para-supersymmetry. Finally, we discuss the hidden SUSY with Z3-graded parity.

We study strings associated with minimal 6d SCFTs, which by definition have only one string charge and no Higgs branch. These theories are labelled by a number n with 1 2 the strings interact with the bulk gauge symmetry. In this paper we find a quiver description for the n = 4 string using Sen's limit of F-theory and calculate its elliptic genus with localization techniques. This result is checked using the duality of F-theory with M-theory and topological string theory whose refined BPS partition function captures the elliptic genus of the SCFT strings. We use the topological string theory to gain insight into the elliptic genus for other values of n.

In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to supergravity amplitudes as a byproduct. At six points, the sources of the hexagon anomaly are identified in superspace as systematic obstructions to BRST invariance. Our results are expected to reproduce any integrated SYM amplitude in dimensions $D< 8$.

This paper addresses a construction of new q-Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self-adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q-deformed boson system is studied.

We analyze the quantum-corrected moduli space of D7-brane position moduli with special emphasis on inflationary model building. D7-brane deformation moduli are key players in two recently proposed inflationary scenarios: The first, D7-brane chaotic inflation, is a variant of axion monodromy inflation which allows for an effective 4d supergravity description. The second, fluxbrane inflation, is a stringy version of D-term hybrid inflation. Both proposals rely on the fact that D7-brane coordinates enjoy a shift-symmetric Kahler potential at large complex structure of the Calabi-Yau threefold, making them naturally lighter than other fields. This shift symmetry is inherited from the mirror-dual Type IIA Wilson line on a D6-brane at large volume. The inflaton mass can be provided by a tree-level term in the flux superpotential. It induces a monodromy and, if tuned to a sufficiently small value, can give rise to a large-field model of inflation. Alternatively, by a sensible flux choice one can completely avoid a tree-level mass term, in which case the inflaton potential is induced via loop corrections. The positive vacuum energy can then be provided by a D-term, leading to a small-field model of hybrid natural inflation. In the present paper, we continue to develop a detailed understanding of the D7-brane moduli space focusing among others on shift-symmetry-preserving flux choices, flux-induced superpotential in Type IIB/F-theory language, and loop corrections. While the inflationary applications represent our main physics motivation, we expect that some of our findings will be useful for other phenomenological issues involving 7-branes in Type IIB/F-theory constructions., 61 pages, 10 figures; v3: references added; v2: references added, error in cosmic string bound corrected

In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe or excitation around some configuration in gauge theory which can be argued to be localized at a particular position in the gravity dual, and match this description to various degrees of accuracy in the gravity dual. The three examples discussed are giant gravitons in $AdS_5\times S^5$, open strings stretching between these giants and the probe dynamics of a D0 brane in the presence of a thermal matrix configuration of the BFSS matrix model.

In this paper we introduce two types of q-deformed Wigner algebras. One is q-deformation of Wigner algebra with q-reflection symmetry and another is q-deformation of Wigner algebra with reflection symmetry. For two types of q-deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q-calculus, we introduce the (q; ν)- numbers, (q; ν)-derivatives and (q; ν)-Hermite polynomials for two algebras. For the deformation parameter q = 1 - ϵ with small ϵ, we discuss the thermodynamics of the particle obeying the q-deformed Wigner algebra.

In this paper, we study peculiar properties of p-wave superconductors in dilaton gravity. The scale invariance of the bulk geometry is effectively broken due to the existence of dilaton. By coupling the dilaton to the non-Abelian gauge field, i.e., $-\frac14 e^{-\beta \Phi} F^a_{\mu\nu}F^{a\mu\nu}$, we find that the dissipative conductivity of the normal phase decreases and approaches zero at the zero frequency as $\beta$ increases. Intuitively, the system behaves more and more like an insulator. When the hairy solution is turned on, the system crosses a critical point to the superconducting phase. We find that the critical chemical potential decreases with the increasing of $\beta$ and the maximum height of the conductivity is suppressed gradually which are consistent with our intuition for insulator/supercondutor transition., Comment: 11 pages, 4 figures

In this paper we address the question how to discriminate whether the gauged isometry group 𝒢Σ of the Kahler manifold Σ that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Σ.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential 𝒦(C) = 2 J(C) where the real scalar field C encodes the inflaton field. As a by product of our analysis we show that phenomenologically admissible potentials for the description of inflation and in particular α-attractors are mostly obtained from the gauging of a parabolic isometry, this being, in particular the case of the Starobinsky model. Yet at least one exception exists of an elliptic α-attractor, so that neither type of isometry can be a priori excluded. The requirement of regularity of the manifold Σ poses instead strong constraints on the α-attractors and reduces their space considerably. Curiously there is a unique integrable α-attractor corresponding to a particular value of this parameter.

We review the concept of anomaly field theory, namely the fact that the anomalies of a $d$-dimensional field theory can be encoded in a $d+1$-dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical facts about anomalies are recovered from the anomaly field theory, and review recent work on global anomaly cancellation in 6d supergravity where this concept was instrumental. We also sketch the status of global anomaly cancellation checks in string theory. This paper is based on a talk given at the Durham Symposium `Higher Structures in M-theory' in August 2018.