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In the AdS/CFT correspondence, states obtained by Hamiltonian evolution of the thermofield doubled state are also dual to an eternal black-hole geometry, which is glued to the boundary with a time shift generated by a large diffeomorphism. We describe gauge-invariant relational observables that probe the black hole interior in these states and constrain their properties using effective field theory. By adapting recent versions of the information paradox we show that these observables are necessarily described by state-dependent bulk-boundary maps, which we construct explicitly. [ABSTRACT FROM AUTHOR]

Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the t channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base slate on the Regge trajectory. To illustrate the procedure, modifications necessary for the process γ + p → K+ Σ+10 are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction. [ABSTRACT FROM AUTHOR]

Recently, Almheiri, Dong, and Harlow have argued that the localization of bulk information in a boundary dual should be understood in terms of quantum error correction. We show that this structure appears naturally when the gauge invariance of the boundary theory is incorporated. This provides a new understanding of the nonuniqueness of the bulk fields (precursors). It suggests a close connection between gauge invariance and the emergence of spacetime. [ABSTRACT FROM AUTHOR]

Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication. [ABSTRACT FROM AUTHOR]

We investigated the appearance of Chern-Simons terms in electrodynamics at the surface or interface of materials. The requirement of locality, gauge invariance, and renormalizability in this model is imposed. Scattering and reflection of electromagnetic waves in three different homogeneous layers of media is determined. Snell's law is preserved. However, the transmission and reflection coefficient depend on the strength of the Chern-Simons interaction (connected with Hall conductance), and parallel and perpendicular components are mixed. [ABSTRACT FROM AUTHOR]

We consider the collective, long-wavelength charge excitations in correlated media in presence of short- and long-range forces. As an example for the case of a short-range interaction, we examine the two-dimensional Hubbard model within dynamical mean-field theory (DMFT). It is shown explicitly that the DMFT susceptibility including vertex corrections respects the Ward identity and yields a manifestly gauge-invariant response in finite dimensions. For computing the susceptibility, we use a different expression and establish its formal equivalence to the standard DMFT formula. It allows for a more stable analytical continuation. We find a zero-sound mode expected for short-range forces. The relation between the vertex corrections, gauge invariance, and the appearance of the collective modes is discussed. Long-range forces are treated within extended dynamical mean-field theory. In order to obtain a gauge-invariant response, it is necessary to additionally incorporate some nonlocal vertex corrections into the polarization. In doing so, we obtain plasmons in the three-dimensional Hubbard model. The plasma frequency is determined by the (single-particle) density distribution as a consequence of gauge invariance. We compare this result with the plasma frequency extracted from the analytical continuation of the susceptibility. It is in good agreement with the prediction from the gauge-invariance condition. [ABSTRACT FROM AUTHOR]

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super- Poincare symmetry. As a concrete example, we focus on the new minimal (12 + 12) off shell version of simple four-dimensional supergravity obtained by tensoring the off shell Yang-Mills multiplets (4 + 4, NL = 1) and (3 + 0, NR = 0). [ABSTRACT FROM AUTHOR]

We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is given by an integral over the positions of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n×2n matrix, ψ, that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian. [ABSTRACT FROM AUTHOR]

Quantum scale invariance in the UV has been recently advocated as an attractive way of solving the gauge hierarchy problem arising in the standard model. We explore the cosmological signatures at the electroweak scale when the breaking of scale invariance originates from a hidden sector and is mediated to the standard model by gauge interactions (gauge mediation). These scenarios, while being hard to distinguish from the standard model at LHC, can give rise to a strong electroweak phase transition leading to the generation of a large stochastic gravitational wave signal in possible reach of future space-based detectors such as eLISA and BBO. This relic would be the cosmological imprint of the breaking of scale invariance in nature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota- equation and the nonintegrable semidiscrete Hirota+ equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota- equation and the nonintegrable semidiscrete Hirota+ equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations. [ABSTRACT FROM AUTHOR]

A one-dimensional electron model with parameters modulated adiabatically in closed cycles is proposed which can continuously pump spin to leads. By defining the spin-polarized Wannier functions, we reveal that the spin pumping is protected by the spin Chern numbers, so that it is stable to perturbations violating the time-reversal symmetry and spin conservation. Our work demonstrates the principle for realizing robust topological spin pumps independent of the time-reversal symmetry. A possible way to directly observe the bulk topological invariants is also suggested. [ABSTRACT FROM AUTHOR]

We consider the nonequilibrium dynamics of a system of interacting massless fermions in a ring threaded by a magnetic flux. We focus on the quench where the flux is initially vanishing and is then turned on. We show that the definition of the limit of abrupt quench is problematic due to the presence of gauge invariance that has to be taken into account. We then propose a specific protocol where the dynamics is nontrivial. Employing techniques coming from the algebraic Bethe ansatz, we present an exact formula for the Loschmidt echo valid at all times as a Fredholm determinant at the free fermionic point. From the analysis of the asymptotic behavior of the Fredholm determinant, we show that the distribution of work done at small energies presents an edge singularity whose exponent can be explicitly computed. Using the correspondence between the edge singularity and the decay of the fidelity at finite size we propose a general formula for the exponent valid also in the interacting case. [ABSTRACT FROM AUTHOR]

We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This presents huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values with respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under a gauge (local) group of dilations. These ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provides some elements that can be used to improve models of animal reproduction. [ABSTRACT FROM AUTHOR]

It is shown that a unitary translationally invariant field theory in 1 + 1 dimensions, satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators, and the requirement that signals propagate with finite velocity, possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies the presence of one or several Lorentz groups acting on the operator algebra of the theory. [ABSTRACT FROM AUTHOR]

Using gauge transformation method, we generate rogue waves for the two-component Bose-Einstein condensates (BECs) governed by the symmetric coupled Gross-Pitaevskii (GP) equations and study their dynamics. We also suggest a mechanism to tame the rogue waves either by manipulating the scattering length through Feshbach resonance or the trapping frequency, a phenomenon not witnessed in the domain of BECs, and we believe that these results may have wider ramifications in the management of rogons. [ABSTRACT FROM AUTHOR]

We formulate the problem of electron transport through an interacting quantum dot system in the framework of the self-consistent perturbation theory of the nonequilibrium Green's function and show that the current conservation through the central region is automatically guaranteed owing to the gauge-invariant properties of the resulting Green's functions and the generalized Ward identity. By using a generating functional for the statistics of the nonequilibrium system, we obtain general formulas for calculating the current and the current fluctuations in the presence of arbitrary time-dependent potentials. As an illustration of application, we study the interaction effects on the finite-frequency noise for electron resonant tunneling through an Anderson impurity and obtain an analytical expression for the finite-frequency current noise within the Hartree approximation, which is an extension of the results obtained by Hershfield on zero-frequency shot noise. [ABSTRACT FROM AUTHOR]

We construct interactions of nucleons N with higher-spin resonances R invariant under point and gauge transformations of the Rarita-Schwinger field. It is found for arbitrarily high spin of a resonance that the requirement of point and gauge invariance uniquely determines a Lagrangian of NR interactions with pions, photons, and vector mesons, which might reduce model ambiguity in effective-field calculations involving such vertices. Considering the NR interactions with photons and vector mesons, the symmetry provides a classification of three NR vertices in terms of their differential order. The Q² dependencies of the point- and gauge-invariant form factors are considered in a vector-meson-dominance model. The model is in good agreement with experimental data. In addition, we point out some empirical patterns in the Q² dependencies of the form factors: low-Q² scaling of the NΔ(1232) form factor ratios and relations between form factors for NN(1520) and NN(1680) transitions. [ABSTRACT FROM AUTHOR]

Dirac electrons in two-dimensional continuum space subject to &function impurities, which have inherent ultraviolet divergence, fail to be gauge-invariant if regularized by the standard momentum (Brillouin-zone) cutoff. A regularization scheme which respects gauge invariance is proposed here based on the cutoff in the impurity-potential range. The relation to a lattice model, which has no ultraviolet divergence, is also discussed. [ABSTRACT FROM AUTHOR]

We propose a model for inflation consisting of an axionic scalar field coupled to a set of three non-Abelian gauge fields. Our model's novel requirement is that the gauge fields begin inflation with a rotationally invariant vacuum expectation value (VEV) that is preserved through identification of SU(2) gauge invariance with rotations in three dimensions. The gauge VEV interacts with the background value of the axion, leading to an attractor solution that exhibits slow roll inflation even when the axion decay constant has a natural value (< MPl). Assuming a sinusoidal potential for the axion, we find that inflation continues until the axionic potential vanishes. The speed at which the axion moves along its potential is modulated by its interactions with the gauge VEV, rather than being determined by the slope of its bare potential. For sub-Planckian axion decay constants vanishingly small tensor to scalar ratios are predicted, a direct consequence of the Lyth bound. The parameter that controls the interaction strength between the axion and the gauge fields requires a technically natural tuning of …(100). [ABSTRACT FROM AUTHOR]

We investigate generic Hamiltonians for confined electrons with weak inhomogeneous spin-orbit coupling. Using a local gauge transformation we show how the SU(2) Hamiltonian structure reduces to a U(1)× U(1) structure for spinless fermions in a fictitious orbital magnetic field, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry or opening additional transport terminals, thus allowing one to switch the generated spin current on or off. We numerically check our theory for mesoscopic cavities as well as Aharonov-Bohm rings [ABSTRACT FROM AUTHOR]

A complete, rigorous relativistic field-theory formulation of the nucleon-nucleon (NN) bremsstrahlung reaction is presented. The resulting amplitude is analytic, Lorentz covariant and unitary as a matter of course and it is gauge invariant; i.e., it satisfies a generalized Ward-Takahashi identity. The novel feature of this approach is the consistent microscopic implementation of local gauge invariance across all interaction mechanisms of the hadronic systems, thus serving as a constraint for all subprocesses. The formalism is quite readily adapted to approximations and thus can be applied even in cases where the microscopic dynamical structure of the underlying interacting hadronic systems is either not known in detail or too complex to be treated in detail. We point out how the interaction currents resulting from the photon being attached to nucleon-nucleon-meson vertices can be treated by phenomenological four-point contact currents that preserve gauge invariance. In an advance application of the present formalism [Nakayama and Haberzettl, Phys. Rev. C 80, 051001(R) (2009)], such interaction currents were found to contribute significantly in explaining experimental data. In addition, we provide a scheme that permits--through an introduction of phenomenological five-point contact currents--the approximate treatment of current contributions resulting from pieces of the NN interaction that cannot be incorporated exactly. In each case, the approximation procedure ensures gauge invanance of the entire bremsstrahlung amplitude. We also discuss the necessary modifications when taking into account baryonic states other than the nucleon N; in detail, we consider the &Dgr;(1232) resonance by incorporating the couplings of the NN to the N&Dgr; and &Dgr;&Dgr; systems and the &ggr;N → &Dgr; transitions. [ABSTRACT FROM AUTHOR]

Using methods of numerical lattice gauge theory we show that, in the limit of a large number of colors, properly regularized Wilson loops have an eigenvalue distribution which changes nonanalytically as the overall size of the loop is increased. This establishes a large-N phase transition in continuum planar gauge theory, a fact whose precise implications remain to be worked out. [ABSTRACT FROM AUTHOR]

It has been shown that a contracting universe with a dustlike (w &ap; 0) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations are amplified. The gauge invariant variable Φ develops a growing mode which becomes much larger than the constant one around the bounce phase. The constant mode has its amplitude fixed by Cosmic Background Explorer (COBE) normalization, thus the amplitude of the growing mode can become much larger than 1. In this paper, we first show that this is a general feature of bouncing models, since we expect that general relativity should be valid in all scales away from the bounce. However, in the Newtonian gauge, the variable Φ gives the value of the metric perturbation &Phi, raising doubts on the validity of the linear perturbative regime at the bounce. In order to address this issue, we obtain a set of necessary conditions for the perturbative series to be valid along the whole history of the model, and we show that there is a gauge in which all these conditions are satisfied, for a set of models, if the constant mode is fixed by COBE normalization. As a by-product of this analysis, we point out that there are sets of solutions for the perturbation variables where some gauge-fixing conditions are not well defined, turning these gauges prohibited for those solutions. [ABSTRACT FROM AUTHOR]

We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure calculation with a coarse ab initio k-point mesh, maximally localized Wannier functions are constructed and used to interpolate the necessary k-space quantities on a fine mesh, in parallel to a previously developed formalism for the anomalous Hall conductivity [X. Wang, J. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B 74, 195118 (2006)]. We formulate our new approach in a manifestly gauge-invariant manner, expressing the orbital magnetization in terms of traces over matrices in Wannier space. Since only a few (e.g., of the order of 20) Wannier functions are typically needed to describe the occupied and partially occupied bands, these Wannier matrices are small, which makes the interpolation itself very efficient. The method has been used to calculate the orbital magnetization of bcc Fe, hep Co, and fee Ni. Unlike an approximate calculation based on integrating orbital currents inside atomic spheres, our results nicely reproduce the experimentally measured ordering of the orbital magnetization in these three materials. [ABSTRACT FROM AUTHOR]

Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required as a step preliminary to the adjustment of the coupling constants. Purpose: We determine to what extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, we study the relations between the validity of the continuity equation and the invariance of the functional under gauge transformations. Methods: We derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the N3LO energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(l) local-gauge-invariance conditions. Conclusions: The validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces. [ABSTRACT FROM AUTHOR]

A general nonlinear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. We consider the application of this theory to a multiterminal mesoscopic system with arbitrary interactions and time-dependent voltages. This allows us to obtain a generalized Kubo-type formula. We derive a microscopic expression for the finite frequency differential conductance matrix, which preserves current conservation and gauge invariance. We exploit this result to show that the asymmetric part of the current fluctuation matrix at finite frequency obeys a generalized time-dependent fluctuation-dissipation theorem. In the stationary regime, this theorem provides a common explanation for the asymmetry of the excess noise with respect to positive and negative frequencies that has been obtained in several systems as a consequence of nonlinearity. It also explains the origin of the unexpected negative sign of the excess noise. Finally, we apply these general results to the case of a tunnel junction and obtain a nonperturbative out-of-equilibrium link between conductance and current fluctuations. We also derive a universal property of the finite frequency noise in the perturbative regime. [ABSTRACT FROM AUTHOR]

We calculate the dc conductivity σ in a pseudogapped high Tc superconductor within a precursor superconductivity theory which is consistent with gauge invariance. Our results contain physical effects beyond those identified previously. Rather than presuming that lifetime effects dominate the T dependence of transport, here we show (consistent with growing experimental support) that the temperature dependence of the effective carrier number is a natural consequence of the pseudogap, and demonstrate reasonable agreement with dc transport in the underdoped cuprates. [ABSTRACT FROM AUTHOR]

We introduce an expression for the ℤ2 topological invariant of band insulators using the non-Abelian Berry connection. Our expression can identify the topological nature of a general band insulator without any of the gauge-fixing problems that plague the concrete implementation of previous invariants. This expression can be derived from the "partner switching" of the Wannier function center during time-reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the Z2 topological index for several topological insulator material systems and obtained consistent results with the previous studies. [ABSTRACT FROM AUTHOR]

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group and non-Abelian Kitaev D(G) models on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wave function for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining or deconfining phase transition of the Wilson loop order parameter. [ABSTRACT FROM AUTHOR]