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We consider couplings of electrically and magnetically charged sources to the maximally symmetric non-linear extension of Maxwell's theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell's electrodynamics. We find that, in contrast to generic models of non-linear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon are exact solutions of the ModMax equations of motion. We then study whether and how ModMax non-linearity affects properties of electromagnetic interactions of charged objects, in particular the Lorentz force, the Coulomb law, the Lienard-Wiechert fields, Dirac's and Schwinger's quantization of electric and magnetic charges, and the Compton Effect. In passing we also present an alternative form of the ModMax Lagrangian in terms of the coupling of Maxwell's theory to axion-dilaton-like auxiliary scalar fields which may be relevant for revealing the effective field theory origin of ModMax., 20 pages, v2: title changed to match the PRD version, typos corrected, references updated

We show that we can interpret the exact solution of the one-dimensional t-J model in the limit of small J in terms of charge carriers with both exchange (braid) and exclusion (Haldane) statistics with parameter 1/2. We discuss an implementation of the same statistics in the two-dimensional t-J model, emphasizing similarities and differences with respect to one dimension. In both cases, the exclusion statistics is a consequence of the no-double occupation constraint. We argue that the application of this formalism to hole-doped high Tc cuprates and the derived composite nature of the hole give a hint to grasp many unusual properties of these materials.

We show that in the $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ spin-charge gauge approach we developed earlier one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers of the $t\text{\ensuremath{-}}J$ model in two dimensions, as it occurs in one dimension. Like the one-dimensional case, the no-double occupation constraint is at the origin of this fractional exclusion statistics. With this statistics we recover a large Fermi volume of holes at high dopings, close to that of the tight binding approximation. Furthermore, the composite nature of the hole, made of charge and spin carriers only weakly bounded, can provide a natural explanation of many unusual experimental features of the hole-doped cuprates.

We show that several features (the three-dimensional XY universality for moderate underdoping, the almost-BCS behaviour for moderate overdoping and the critical exponent) of the superfluid density in hole-doped cuprates hint at a composite structure of the holes. This idea can be implemented in a spin-charge gauge approach to the $t - t' - J$ model and provides indeed good agreement with available experimental data., 5 pages, 1 figure, to be published in the proceedings of the International Conference in Superconductivty and Magnetism ICSM2016

In high-$T_c$ cuprates many quantities exhibit a non-Fermi liquid universality hinting at a very peculiar structure of the underlying pairing mechanism for superconductivity: in this work we focus on the universality for the in-plane resistivity and for the superfluid density. We outline the previously developed spin-charge gauge approach to superconductivity in hole-doped cuprates: we decompose the hole of the $t-t'-J$ model for the $\mathrm{Cu}\mathrm{O}_2$ planes as the product of a spinful, chargeless gapped spinon and of a spinless, charged holon with Fermi surface. Each one of these particle excitations is bound to a statistical gauge flux, allowing one to optimize their statistics. We show that this model allows for a natural interpretation of the universality: within this approach, under suitable conditions, the spinonic and holonic contributions to a response function sum up according to a Ioffe-Larkin rule. We argue that, if the spinonic contribution dominates, then one should expect strongly non-Fermi-liquid-like universality, due to the insensitivity of spinons to Fermi surface details. The in-plane resistivity and superfluid density are indeed dominated by the spinons in the underdoped region. We theoretically derive these quantities, discussing their universal behaviours and comparing them with experimental data., 16 pages, 3 figures, to be published in a Festschrift issue of Journal of Low Temperature Physics in honor of Prof. Flavio Toigo on the occasion of his 70th birthday

Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. The gluing force of the superconducting mechanism is an attraction between spin vortices on two different N\'eel sublattices, centered around the empty sites described in terms of fermionic holons. The spin fluctuations are described by bosonic spinons with a gap generated by the spin vortices. Due to the no-double occupation constraint, there is a gauge attraction between holon and spinon binding them into a physical hole. Through gauge interaction the spin vortex attraction induces the formation of spin-singlet (RVB) spin pairs with a owering of the spinon gap. Lowering the temperature the approach exhibits two crossover temperatures: at the higher crossover a finite density of incoherent holon pairs are formed leading to a reduction of the hole spectral weight, at the lower crossover also a finite density of incoherent spinon RVB pairs are formed, giving rise to a gas of incoherent preformed hole pairs, and magnetic vortices appear in the plasma phase. Finally, at a even lower temperature the hole pairs become coherent, the magnetic vortices become dilute and superconductivity appears. The superconducting mechanism is not of BCS-type since it involves a gain in kinetic energy (for spinons) coming from the spin interactions., Comment: 4 pages, 3 figures, accepted by the proceedings of SNS2010 conference

Spin-statistics transmutation is the phenomenon occurring when a “dressing” transformation introduced for physical reasons (e.g. gauge invariance) modifies the “bare” spin and statistics of particles or fields. Historically, it first appeared in Quantum Mechanics and in semiclassical approximation to Quantum Field Theory. After a brief historical introduction, we sketch how to describe such phenomenon in Quantum Field Theory beyond the semiclassical approximation, using a path-integral formulation of euclidean correlation functions, exemplifying with anyons, dyons and skyrmions.

We prove that a gauge approach based on a composite structure of the hole in hole-doped cuprates is able to capture analytically many features of the experimental data on superfluid density in the moderate-underdoping to nearly-optimal doping region, including critical exponent, the Uemura relation and near universality of the normalized superfluid density., Comment: 13 pages, 2 figures, accepted for publication in EPL

Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations, and show that even moderate nonlinearities in the spectrum can yield substantial deviations from the standard result. We apply our result to an attractive Fermi gas in the BCS-BEC crossover: here the low-energy bosonic collective excitations are density oscillations driven by the phase of the pairing order field. These collective excitations, which are gapless modes as a consequence of the Goldstone mechanism, have a spectrum which is well established both theoretically and experimentally, and whose linewidth, we show, is determined at low temperatures by the Beliaev decay mechanism., Comment: 8 pages, 3 figures

We clarify the relation between two kinds of statistics for particle excitations in planar systems: the braid statistics of anyons and the Haldane exclusion statistics(HES). It is shown non-perturbatively that the HES exists for incompressible anyon liquid in the presence of a Hall response. We also study the statistical properties of a specific quantum anomalous Hall model with Chern-Simons term by perturbation in both compressible and incompressible regimes, where the crucial role of edge states to the HES is shown.

We review a recently proposed mechanism for superconductivity in hole-doped cuprates exhibiting a strong interplay between pairing and antiferromagnetism. Starting from the t-t'-J model for the CuO planes, we show that this interplay can explain in a unified framework the pseudogap phenomenology of the spectral weight of the hole, the hourglass-like structure of the magnetic excitation, the critical exponent of the superfluid density, the relation between the scale of the magnetic resonance and Tc., 2 figures, talk given at the International Conference in Superconductivty and Magnetism ICSM2014-Antalya

Based on recently proposed U(1) × SU(2) Chern-Simons gauge field theory, an interpretation of the transport and magnetic relaxation properties of underdoped cuprates is proposed. The interplay of the doping-dependent spin gap effect and dissipation due to gauge fluctuations gives rise to a crossover from metallic to insulating behavior of conductivity as temperature decreases, in semi-quantitative agreement with experimental data. For the same reason the magnetic relaxation rate shows a maximum nearby.

We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST-mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac-Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical field theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac-string. Nevertheless, the Quantum Field Theory, obtained from this classical action via a functional integral approach, turns out to be independent of the particular vector field chosen, and thus consistent, if the Dirac-Schwinger quantization condition holds. We provide explicit expressions for the generating functionals of observables, proving that they are Dirac-string independent. Since Lorentz-invariance is manifest at each step, the quantum theory admits also a manifestly diffeomorphism invariant coupling to external gravity. Relations with previous formulations, and with SO(2)--non invariant theories are clarified., 49 pages, LaTeX, no figures

We show that the spin–charge gauge approach to the 2D t – J model can naturally explain many experimental features of transport properties for HTS cuprates, in particular temperature crossover phenomena in the “pseudogap phase” (PG) and 1/ T behavior of conductivities in the “strange metal phase” (SM) at higher T or x (doping concentration).

The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to the two-dimensional t-J model in the limit t much greater than J, to study the normal-state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background and we find the optimal spinon configuration saturating the upper bound on average-a coexisting flux phase and s+id-like resonating-valence-bond state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V, the holon field is a fermion and the spinon field is a hard-core boson. Within this approximation we show that the B field produces a rr flux phase for the holons, converting them into Dirac-like fermions, while the V field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero-doping limit. The nonlinear-a model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long-range AF order in reference compounds. Moreover, we derive a low-energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi-liquid theory with a Fermi surface consisting of four "half-pockets" centered at (+/-pi/2,+/-pi/2) and one reproduces the results for the electron spectral function obtained in the mean-field approximation, in agreement with the photoemission data on underdoped cuprates: The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalization effects due to gauge fluctuations give rise to non-Fermi-liquid behavior for the composite electron, in certain temperature range showing the linear in T resistivity. This formalism provides a new interpretation of the spin gap in the underdoped superconductors (mainly due to the short-ranged AF order) and predicts that the minimal gap for the physical electron is proportional to the square root of the doping concentration. Therefore the gap does not vanish in any direction. All these predictions can be checked explicitly in experiment.

The $U(1)\times SU(2)$ Chern-Simons gauge theory is applied to study the 2-D $t-J$ model describing the normal state of underdoped cuprate superconductors. The U(1) field produces a flux phase for holons converting them into Dirac-like fermions, while the SU(2) field, due to the coupling to holons gives rise to a gap for spinons. An effective low-energy action involving holons, spinons and a self-generated U(1) gauge field is derived. The Fermi surface and electron spectral function obtained are consistent with photoemission experiments. The theory predicts a minimal gap proportional to doping concentration. It also explains anomalous transport properties including linear $T$ dependence of the in-plane resistivity., Comment: 8 pages, REVTEX, no figures

We propose an explanation of several experimental features of transport phenomena in the normal state of high Tc cuprates in terms of a spin-charge gauge theory of the 2D t-J model. The calculated doping-temperature dependence for a number of physical quantities is found in qualitative agreement with data. In particular, we recover: in the ``pseudogap phase'' the metal-insulator crossover of the in-plane resistivity and of the NMR ``relaxation time'' and the insulating behavior of the out-of-plane resistivity; in the ``strange metal phase'' (at higher temperature or doping) the linear in T behavior of the above quantities; the appearance of maxima in the in-plane far-infrared conductivity in strongly underdoped and overdoped samples., Comment: 8 pages, 14 figures; to appear without figures in Journal of Physics and Chemistry of Solids

We study finite-temperature properties of a two-dimensional superfluid made of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the region below the critical temperature $T_{BKT}$ of the Berezinskii-Kosterlitz-Thouless phase transition, where there is quasi-condensation, by analyzing the effects of phase and amplitude fluctuations of the order parameter. In particular, we calculate the superfluid fraction, the sound velocity and the quasi-condensate fraction as a function of the temperature and of the binding energy of fermionic pairs.

We perform a dimensional reduction of the $U(1)\times SU(2)$ Chern--Simons bosonization and apply it to the $t-J$ model, relevant for high $T_c$ superconductors. This procedure yields a decomposition of the electron field into a product of two ``semionic" fields, i.e. fields obeying abelian braid statistics with statistics parameter $��={1\over 4}$, one carrying the charge and the other the spin degrees of freedom. A mean field theory is then shown to reproduce correctly the large distance behaviour of the correlation functions of the 1D $t-J$ model at $t>>J$. This result shows that to capture the essential physical properties of the model one needs a specific ``semionic" form of spin--charge separation., 31 pages, Plain TeX, no figures

We assume the t-t'-J model to describe the CuO_2 planes of hole-doped cuprates and we adapt the spin-charge gauge approach, previously developed for the t-J model, to describe the holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of a finite density of incoherent holon pairs in the normal state. Below a crossover temperature, identified as the experimental "upper pseudogap", the scattering of the "quanta" of the phase of the holon-pair field against holons reproduces the phenomenology of Fermi arcs coexisting with gap in the antinodal region. We thus obtain a microscopic derivation of the main features of the hole spectra due to pseudogap. This result is obtained through a holon Green function which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like and a d-wave superconductor behavior as the coherence length of the holon pair order parameter increases. By inserting the gauge coupling with the spinon we construct explicitly the hole Green function and calculate its spectral weight and the corresponding density of states. So we prove that the formation of holon pairs induces a depletion of states on the hole Fermi surface. We compare our results with ARPES and tunneling experimental data. In our approach the hole preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Therefore we propose that the gap seen in the normal phase of cuprates is due to the thermal broadening of the SC-like peaks masking the Fermi-liquid peak. The Fermi arcs then correspond to the region of the Fermi surface where the Fermi-liquid peak is unmasked., Comment: 10 figures, comments and references added, 2 figures changed

We propose a non-BCS mechanism for superconductivity in hole-underdoped cuprates based on a gauge approach to the {\it t-J} model. The gluing force is an attraction between spin vortices centered on the empty sites of two opposite N\'eel sublattices, leading to pairing of charge carriers. In the presence of these pairs, a gauge force coming from the single occupancy constraint induces, in turn, the pairing of the spin carriers. The combination of the charge and spin pairs gives rise to a finite density of incoherent hole pairs, leading to a finite Nernst signal as precursor to superconductivity. The true superconducting transition occurs at an even lower temperature, via a 3D XY-type transition. The main features of this non-BCS description of superconductivity are consistent with the experimental results in underdoped cuprates, especially the contour plot of the Nernst signal., Comment: 6 pages, 1 figure, accepted by EPL

Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. We implement the no-double occupancy constraint with a (semionic) slave-particle formalism. The dopant generates a vortex-like quantum distortion of the AF background centered on the empty sites, with opposite chirality for cores on the two N\'eel sublattices. Empty sites are described in terms of spinless fermionic holons and the long-range attraction between spin vortices on two opposite N\'eel sublattices is the holon pairing force, leading eventually to SC. The spin fluctuations are described by bosonic spinons with a gap generated by scattering on spin vortices. Due to the occupation constraint, there is a gauge attraction between holon and spinon, binding them into a physical hole. Through gauge interaction the spin vortex attraction induces the formation of spin-singlet RVB pairs reducing the spinon gap. Lowering T, there are two crossovers as precursors of the SC transition: at the higher one a gas of holon pairs appears, reducing the hole spectral weight, while at the lower one a gas of spinon pairs also appears, giving rise to a gas of incoherent preformed hole pairs with magnetic vortices in the plasma phase, supporting a Nernst signal. At an even lower T the hole pairs become coherent and SC appears beyond a critical doping. The proposed SC mechanism is not of the BCS-type, because it involves a gain in kinetic energy (lowering of spinon gap) and it is "almost" of the classical 3D XY-type. Since both the spinon gap and the holon pairing originate from the same term in the slave-particle representation of the t-J model, this approach incorporates a strong interplay between AF and SC, giving rise to a universal relation between Tc and the energy of the resonance mode, as observed in neutron scattering experiments., Comment: 19 pages, 6 figures

Within the framework of the spin–charge gauge approach to the 2D t – J model (Marchetti et al., 2007 [1] ) we propose a new non-BCS mechanism for superconductivity in hole-underdoped cuprates. The gluing force is an attraction between spin-vortices centered at the empty sites (described by fermionic holons) in two different Neel sublattices. This attraction induces in turn, through a gauge interaction originated from the no-double occupation constraint, formation of resonance valent bond (RVB) spin pairs (described in terms of bosonic spinons). When holon pairs condense, a finite density of RVB spinon pairs appears. Superconductivity occurs at T = 0 at finite doping concentration, when both the holon-vortex pairs and the RVB spinon pairs are condensed. Its precursor is a normal state region where magnetic vortices proliferate, leading to superconductivity via a 3D-gauged-XY transition.

We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or “isospin” S = 1 2 , 3 3 , 5 2 ,… confined to a plane (e.g. a heterojuncture) can be described in terms of a complex boson of spin or isospin S coupled to statistical U(1) and SU(2) gauge fields. In a Feynman path integral formulation, the U(1) gauge field has a Chern-Simons action with coupling constant k = 2 (2l + 1) , l = 0, 1, 2,… , while the SU(2) gauge field has a Chern-Simons action with level 2 S . Generalizations to internal symmetry groups other than SU(2) are sketched, and applications of our formalism to an analysis of excitations with braid statistics in incompressible quantum fluids and of holons and spinons in the t − J model are discussed.

We further develop the general theory of superselection sectors and their statistics for quantum fields on three-dimensional space-time. We show that the statistics of particles that are not localizable in bounded regions of space-time (but in space-like cones) are described by braid-group, rather than permutation-group representations, unless their spins are integral or half-integral. A general connection between spin and statistics is established. Extensions of the theory to non-relativistic systems of two-dimensional condensed matter physics are sketched which makes it applicable to the fractional quantum Hall effect and certain models of high- T c superconductivity.

Many experimental features of the electronic specific heat and entropy of high Tc cuprates in the normal state, including the nontrivial temperature dependence of the specific heat coefficient and negative intercept of the extrapolated entropy to T=0 for underdoped cuprates, are reproduced using the spin-charge gauge approach to the t-J model. The entropy turns out to be basically due to fermionic excitations, but with a temperature dependence of the specific heat coefficient controlled by fluctuations of a gauge field coupling them to gapful bosonic excitations. In particular the negative intercept of the extrapolated entropy at T=0 in the pseudogap ``phase'' is attributed to the scalar component of the gauge field, which implements the local no-double occupancy constraint., Comment: 5 pages, 5 figures

The spin-charge gauge approach to consider the metal-insulator crossover (MIC) and other anomalous transport properties in High-T$_c$ cuprates is briefly reviewed. A U(1) field gauging the global charge symmetry and an SU(2) field gauging the global spin-rotational symmetry are introduced to study the two-dimensional $t-J$ model in the limit $t\gg J$. The MIC as a clue to the understanding of the ``pseudogap'' (PG) phase, is attributed to the competition between the short-range antiferromagnetic order and dissipative motion of charge carriers coupled to the slave-particle gauge field. The composite particle formed by binding the charge carrier (holon) and spin excitation (spinon) via the slave particle gauge field exhibits a number of peculiar properties, and the calculated results are in good agreement with experimental data for both PG and ``strange metal'' phases. Connections to other gauge field approaches in studying the strong correlation problem are also briefly outlined., Comment: 32 pages, to appear in the special issue on "Correlated Electrons" of J. Phys.: Condens. Matt

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical Electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions., 36 pages, no figures, refs. and comments added

We propose an explanation of several experimental features related to the "pseudogap" in high T-c cuprates in terms of a spin-charge gauge theory. In this approach, based on a formal spin-charge separation applied to the t-J model, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap m(s) similar to J(delta\ ln delta\)(1/2), where delta is the doping concentration) and holons with "small" Fermi surface (epsilon(F) similar to tdelta) interacting via a gauge field. The main effect of gauge fluctuations is to introduce a dissipation similar to T/chi where chi is the diamagnetic susceptibility. The competition between the two energy scales, in, and T/chi is the root in our approach of many phenomena peculiar to transport properties of the "pseudogap phase". A good agreement is found between the experimental data and theoretically derived doping and temperature dependence of many physical quantities, such as in-plane and out-of-plane resistivity, in-plane magnetoresistance, far infrared electronic AC conductivity and spin lattice relaxation rate. (C) 2004 Elsevier B.V. All rights reserved.

We describe a monopole-like order parameter for the confinement-deconfinement transition in gauge theories where dynamical charges and monopoles coexist. It has been recently proposed in a collaboration with J. Froehlich. It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for electromagnetic fluxes. An application to SU(2) lattice Yang-Mills theory is outlined, naturally fitting in the 't Hooft scenario for confinement., Comment: LaTeX file, 4 pages. Talk given at QCD 02 (Montpellier 2-9 july 2002)

This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of ``unobservability'' of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts., Comment: LaTex, 39 pages, references and comments added

The metal-insulator crossover of the in-plane resistivity upon temperature decrease, recently observed in several classes of cuprate superconductors, when a strong magnetic field suppresses the superconductivity, is explained using the $U(1)\times SU(2)$ Chern-Simons gauge field theory. The origin of this crossover is the same as that for a similar phenomenon observed in heavily underdoped cuprates without magnetic field. It is due to the interplay between the diffusive motion of the charge carriers and the ``peculiar'' localization effect due to short-range antiferromagnetic order. We also calculate the in-plane transverse magnetoresistance which is in a fairly good agreement with available experimental data., 4 pages, 3 .eps figures, to appear in Physical Review Letters

The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as "building blocks": i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of "characteristic currents" ii) the PST formalism . As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D=10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M.Tonin, where however still as open problem remains a Dirac anomaly., Comment: LaTeX file, espcrc2.sty, 6 pages. Based on the talk given by P.M. at the D.V. Volkov Memorial Conference "Supersymmetry and Quantum Field Theory" (25-29 July, 2000, Kharkov, Ukraine). To be published in Nuclear Physics B Conference Supplements

This paper presents a general covariant lagrangian framework for the dynamics of a system of closed n-branes and dual (D-n-4)-branes in D dimensions, interacting with a dynamical (n+1)-form gauge potential. The framework proves sufficiently general to include also a coupling of the branes to (the bosonic sector of) a dynamical supergravity theory. We provide a manifestly Lorentz-invariant and S-duality symmetric Lagrangian, involving the (n+1)-form gauge potential and its dual (D-n-3)-form gauge potential in a symmetric way. The corresponding action depends on generalized Dirac-strings. The requirement of string-independence of the action leads to Dirac-Schwinger quantization conditions for the charges of branes and dual branes, but produces also additional constraints on the possible interactions. It turns out that a system of interacting dyonic branes admits two quantum mechanically inequivalent formulations, involving inequivalent quantization conditions. Asymmetric formulations involving only a single vector potential are also given. For the special cases of dyonic branes in even dimensions known results are easily recovered. As a relevant application of the method we write an effective action which implements the inflow anomaly cancellation mechanism for interacting heterotic strings and five-branes in D=10. A consistent realization of this mechanism requires, in fact, dynamical p-form potentials and a systematic introduction of Dirac-strings., 36 pages, LaTeX, no figures

We analyse spin and statistics of quantum dyon fields, i.e. fields carrying both electric and magnetic charge, in 3+1 space-time dimensions. It has been shown long time ago that, at the quantum mechanical level, a composite dyon made out of a magnetic pole of charge g and a particle of electric charge e possesses half-integral spin and fermionic statistics, if the constituents are bosons and the Dirac quantization condition $eg=2\pi n$ holds, with n odd. This phenomenon is called spin-statistics transmutation. We show that the same phenomenon occurs at the quantum field theory level for an elementary dyon. This analysis requires the construction of gauge invariant charged dyon fields. Dirac's proposal for such fields, relying on a Coulomb-like photon cloud, leads to quantum correlators exhibiting an unphysical dependence on the Dirac-string. Recently Froehlich and Marchetti proposed a recipe for charged dyon fields, based on a sum over Mandelstam-strings, which overcomes this problem. Using this recipe we derive explicit expressions for the quantum field theory correlators and we provide a proof of the occurrence of spin-statistics transmutation. The proof reduces to a computation of the self-linking numbers of dyon worldlines and Mandelstam strings, projected on a fixed time three-space. Dyon composites are also analysed. The transmutation discussed in this paper bares some analogy with the appearance of anomalous spin and statistics for particles or vortices in Chern-Simons theories in 2+1 dimensions. However, peculiar features appear in 3+1 dimensions e.g. in the spin addition rule., Comment: 32 pages, LaTeX, no figures

Based on recently proposed U(1)xSU(2) Chern-Simons gauge field theory, an interpretation of the transport and magnetic relaxation properties of underdoped cuprates is proposed, taking into account the short range antiferromagnetic order. The interplay of the doping-dependent spin gap (explicitly derived by us) effect and dissipation due to gauge fluctuations gives rise to a crossover from metallic to insulating behavior of conductivity as temperature decreases, in semi-quantitative agreement with experimental data. For the same reason the magnetic relaxation rate shows a maximum nearby. Various crossover temperatures related to spin gap effects are shown to be different manifestations of the same energy scale., 4 pages with three .eps figures

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem., Comment: 10 pages, Latex file

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the electron degrees of freedom we obtain the effective action forA. We show that, in the scaling limit, this effective action is quadratic inA and can be viewed as an integral over the Fermi sphere of effective actions of (1+1)-dimensional, chiral schwinger models. We use this result to elucidate Luther-Haldane bosonization of systems of non-relativistic electrons. We also study systems of weakly coupled interacting electrons for which the BCS channel is turned off. Using the quadratic dependence of the effective action onA, we show that, in the scaling limit, the RPA yields the dominant contribution.

We consider a model of 2D gravity with the coefficient of the Einstein-Hilbert action having an imaginary part $\pi/2$. This is equivalent to introduce a $\Theta$-vacuum structure in the genus expansion whose effect is to convert the expansion into a series of alternating signs, presumably Borel summable. We show that the specific heat of the model has a physical behaviour. It can be represented nonperturbatively as a series in terms of integrals over moduli spaces of punctured spheres and the sum of the series can be rewritten as a unique integral over a suitable moduli space of infinitely punctured spheres. This is an explicit realization \`a la Friedan-Shenker of 2D quantum gravity. We conjecture that the expansion in terms of punctures and the genus expansion can be derived using the Duistermaat-Heckman theorem. We briefly analyze expansions in terms of punctured spheres also for multicritical models., Comment: 12 pages + 2 figures available upon request. LaTeX File

We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''

We discuss the particle structure in the soliton sectors of massive lattice field theories by means of convergent cluster expansions. In several models we prove that the soliton field operator with lowest charge couples the vacuum to a stable one-particle state, in a suitable region of the coupling parameter space. Both local and stringlike solitons are analyzed. We also show that the mass of the local soliton equals the surface tension.

For a Minkowski spacetime of dimension three, particles of arbitrary, real spin and intermediate (ϑ-) statistics, called ‘anyons’, are studied within the framework of relativistic quantum field theory. The localization properties of interpolating fields for anyons and the relation between the spin of anyons and their statistics are discussed on general grounds. A model of a quantum field theory exhibiting anyons is described. Our results might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of high-T c superconductors.

We show that a process of concentration of baryon number (B) into restricted volumes, during the cosmological quark-hadron transition (Witten effect), should be present even if the transition temperature Tc exceeds 100 MeV and, rather, is stronger for higher Tc. If, however, quark nuggets do not form and B concentrations finally consist of large and localized baryon density peaks there still may be significant consequences for primeval nucleosynthesis and, in particular, present estimated limits on baryonic matter density, worked out from observed light element abundances, should be rediscussed.

We construct physical states of arbitrary magnetic charge for the U(1)4 lattice gauge theory and electrically charged states for the four-dimensional, noncompact Abelian Higgs model, or spinor QED, in the massless QED phase of these models. We discuss the infraparticle structure of monopoles and charged particles and show that, in the continuum limit (if it exists), the Lorentz group cannot be implemented unitarily on charged sectors.

Quantization of solitons in terms of Euclidean region functional integrals is developed, and Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The quantization method is applied to several lattice field theories with solitons, and the particle structure in the soliton sectors of such theories is analyzed. A construction of magnetic monopoles in the four-dimensional, compactU(1)-model, in the QED phase, is indicated as well.

The Abelian gauge quantum field theories of skew-symmetric tensor fields are reviewed in the fremework of the superfield formalism previously proposed. The BRS invariance properties of those theories and the role of the secondary ghosts are discussed.