Studies about a formal analogy between the gravitational and the electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. In fact, the GEM equations correspond to the weak field approximation of gravitation field. Here a non-abelian extension of the GEM theory is considered. Using the Thermo Field Dynamics (TFD) formalism to introduce temperature effects some interesting physical phenomena are investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect at zero and finite temperature for this non-abelian field are calculated.
The Gravitoelectromagnetism (GEM) theory is considered in a lagrangian formulation using the Weyl tensor components. A perturbative approach to calculate processes at zero temperature has been used. Here the GEM at finite temperature is analyzed using Thermo Field Dynamics, real time finite temperature quantum field theory. Transition amplitudes involving gravitons, fermions and photons are calculated for various processes. These amplitudes are likely of interest in astrophysics.
The standard model and general relativity are local Lorentz invariants. However it is possible that at Planck scale there may be a breakdown of Lorentz symmetry. Models with Lorentz violation are constructed using Standard Model Extension (SME). Here gravitational sector of the SME is considered to analyze the Lorentz violation in Gravitoelectromagnetism (GEM). Using the energy-momentum tensor, the Stefan-Boltzmann law and Casimir effect are calculated at finite temperature to ascertain the level of local Lorentz violation. Thermo Field Dynamics (TFD) formalism is used to introduce temperature…
Gravitoelectromagnetism (GEM) is an approach for the gravitation field that is described using the formulation and terminology similar to that of electromagnetism. The Lorentz violation is considered in the formulation of GEM that is covariant in its form. In practice such a small violation of the Lorentz symmetry may be expected in a unified theory at very high energy. In this paper a non-minimal coupling term, which exhibits Lorentz violation, is added as a new term in the covariant form. The differential cross section for Bhabha scattering in the GEM framework at finite temperature is calcu…
The energy-momentum tensor for the gravitoelectromagnetism (GEM) theory in the real-time finite temperature field theory formalism is presented. Expressions for the Casimir energy and pressure at zero and finite temperature are obtained. An analysis of the Casimir effect for the GEM field is developed.
We compute the exact canonically induced parity breaking part of the effective action for 2+1 massive fermions in particular Abelian and non Abelian gauge field backgrounds. The method of computation resorts to the chiral anomaly of the dimensionally reduced theory.
The Yang-Mills-aether theory is considered. Implications of the non-abelian aether-like term, which introduces violation of Lorentz symmetry, is investigated in a thermal quantum field theory. The Thermofield Dynamics formalism is used to introduce the temperature effects and spatial compactification. As a consequence, corrections due to the non-abelian aether term are calculated for the non-abelian Stefan-Boltzmann law and for the non-abelian Casimir energy and pressure at zero and finite temperature.
We show that when the Abelian \CS\ theory coupled to matter fields is quantized in a vacuum with non vanishing magnetic flux (or electric charge), the requirement of gauge invariance at finite temperature leads to the quantization of the \CS\ coefficient and its quantum corrections, in a manner similar to the non-Abelian case.
Following our earlier investigations we examine the quantum-classical winding number transition in the Abelian-Higgs system. It is demonstrated that the sphaleron transition in this system is of the smooth second order type in the full range of parameter space. Comparison of the action of classical vortices with that of the sphaleron supports our finding.
We explore the low-temperature behavior of the Abelian Higgs model in AdS_4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the charge of the scalar is not too small, we observe at low temperatures the emergence of a domain wall structure characterized by a definite index of refraction. We also compute the conductivity as a function of frequency…
In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of 1+1 dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum correc…
Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function regularization is revisited and extended in order to provide a general framework for further applications. A field theoretical model - called extended higher-abelian Maxwell theory - is introduced, which is a higher-abelian version of Maxwell theory of electromagnetism extended by a particular topological action. This action is parametrized by two non-dynamical ha…
We discuss several different constructions of non-Abelian large gauge transformations at finite temperature. Pisarski's ansatz with even winding number is related to Hopf mappings, and we present a simple new ansatz that has any integer winding number at finite temperature.
We calculate the exact parity odd part of the effective action ($Γ_{odd}^{2d+1}$) for massive Dirac fermions in 2d+1 dimensions at finite temperature, for a certain class of gauge field configurations. We consider first Abelian external gauge fields, and then we deal with the case of a non-Abelian gauge group containing an Abelian U(1) subgroup. For both cases, it is possible to show that the result depends on topological invariants of the gauge field configurations, and that the gauge transformation properties of $Γ_{odd}^{2d+1}$ depend only on those invariants and on the winding number of th…
In this paper we study the effects of a nonzero chemical potential in the effective action for massless fermions in (1+1) dimensions in an abelian gauge field background at finite temperature. We calculate the n-point function and show that the structure of the amplitudes corresponds to a generalization of the structure noted earlier in a calculation without a chemical potential (the associated integrals carry the dependence on the chemical potential). Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. However, unlike the …
A four-dimensional Lorentz-breaking non-Abelian Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to the spinor field. This term is shown to be regularization dependent but nevertheless it can be found unambiguously in different regularization schemes at zero and finite temperature.
We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find…
We describe the relationship between time-ordered and retarded response functions in a plasma. We obtain an expression, including the proper $iε$-prescription, for the induced current due to hard thermal loops in a non-Abelian theory, thus giving the non-Abelian generalization of the Kubo formula. The result is closely related to the eikonal for a Chern-Simons theory and is relevant for a gauge-invariant description of Landau damping in the quark-gluon plasma at high temperature.
An abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-abelian gauge fields. There is a second order phase transition between Reissner-Nordstrom-anti-de Sitter solutions, which are preferred at high temperatures, and symmetry breaking solutions, which are preferred at low temperatures.
We test a new parametrization of a suitably truncated classically perfect action for SU(2) pure gauge theory with respect to self-consistency and locate the deconfinement transition on a 12^3X4 lattice. Using the technique of smoothing (blocking followed by inverse blocking) we demonstrate clustering of action and topological charge density. Concentrating on the Abelian monopoles found in smoothed configurations after Abelian projection from the maximally Abelian gauge, we present evidence for their role as carriers of non-Abelian action and topological charge.
We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition…
Gauge fixing and the observable fields for both abelian and non-abelian gauge theories with spontaneous breaking of gauge symmetry are studied. We explicitly show that it is possible to globally fix the gauge in the broken sector and hence construct physical fields even in the non-abelian theory. We predict that any high temperature restoration of gauge symmetry will be accompanied by a confining transition.
We derive an induced Abelian Chern-Simons (CS) term in 2+1 dimensions, by dimensional reduction from the finite-temperature theory of a Dirac field with both vector and axial-vector couplings to two Abelian gauge fields, in 3+1 dimensions. In our construction, the CS term emerges for the lowest Matsubara mode of the vector Abelian field, by integrating the fermionic field, under the assumption that the axial vector field is in a "vacuum" configuration. This configuration is characterized by a single number, which in turn determines the coefficient of the induced CS term for the Abelian vector …
We test at the electroweak scale the recently proposed elaborate theoretical scenario for real-time dynamics of non-abelian gauge theories at high temperature. We see no sign of the predicted behavior. This indicates that perturbative concepts like color conductivity and Landau damping might be irrelevant at temperatures corresponding to the electroweak scale.
In this letter we discuss the influence of a U(1) chemical potential $μ$ on the existence of Gribov copies in a U(1) theory at finite temperature $T$. We show that the chemical potential conspires against the existence of Gribov copies in the sense that it restricts the space of solutions of the consistency equation for the gauge parameter. Explicit solutions are found for T=0, as function of $μ$. In the finite temperature case we find also a class of solutions which satisfy the KMS boundary conditions in the euclidean time direction, having also a vanishing behavior when $|\mathbf r|\to\infty…
The phase structure of a non-isotropic non-Abelian SU(3) lattice gauge model at finite temperature is investigated to the third order in the variational-cumulant expansion (VCE) approach. The layer phase exists in this model in the cases of dimensions D=4, D=5 (d=D-1).
We consider time dependent correlation functions of non-abelian gauge fields at finite temperature. An effective theory for the soft ($p\sim g^2 T$) field modes is derived by integrating out the field modes with momenta of order $T$ and of order $g T$ in a leading logarithmic approximation. In this effective theory the time evolution of the soft fields is determined by a local Langevin-type equation. As an application, the rate for hot electroweak baryon number violation is estimated as $Γ\sim g^2 \log(1/g) (g^2 T)^4$. Furthermore, possible consequences for non-perturbative lattice computation…
We study a three dimensional Abelian Higgs model containing singly- and doubly-charged scalar fields coupled to a compact Abelian gauge field in the London limit. The model attracts interest because of its relevance to high-Tc superconductors with charge 1 holon and charge 2 spinon-pair fields. It contains two types of vortices carrying magnetic flux and one type of instanton-like monopoles. Using thermodynamic and topological observables we present the phase diagram in the parameter space of the gauge and holon and spinon-pair couplings. The Fermi liquid, the spin gap, the superconductor and …
Leading-log results are derived for the shear viscosity, electrical conductivity, and flavor diffusion constants in both Abelian and non-Abelian high temperature gauge theories with various matter field content.
The dynamics of soft ($|\vec{p}|\sim g^2 T$) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta $p_0\lsim g^2 T$, $|\vec{p}|\sim g^2 T$ and loop momenta larger than $g^2 T$. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order $T$. There are higher loop diagrams, involving also the scale $gT$, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories …
We study the phase structure of a three dimensional Abelian Higgs model with singly- and doubly-charged scalar fields coupled to a compact Abelian gauge field. The model is pretending to describe systems of strongly correlated electrons such as high-Tc superconductivity in overdoped regime and exotic phases supporting excitations with fractionalized quantum numbers. We identify the Fermi liquid, the spin gap, the superconductor and the strange metallic phases in which densities and properties of holon and spinon vortices and monopoles are explored. The phase diagram in the 3D coupling space is…
We present arguments for the existence of higher dimensional asymptotically AdS non Abelian black holes with a Ricci flat event horizon and analyze their basic properties. Unlike higher dimensional black holes with a curved horizon, of the usual Einstein-Yang-Mills system, these solutions have finite mass-energy. Below some non-zero critical temperature, they are thermodynamically preferred over the Abelian configurations.
We construct finite mass, asymptotically flat black hole solutions in d=4 Einstein-Yang-Mills theory augmented with higher order curvature terms of the gauge field. They possess non-Abelian hair in addition to Coulomb electric charge, and, below some non-zero critical temperature, they are thermodynamically preferred over the Reissner-Nordstrom solution. Our results indicate the existence of hairy non-Abelian black holes which are stable under linear, spherically symmetric perturbations.
We point out that non-Abelian sine-Gordon solitons stably exist in the $U(N)$ chiral Lagrangian. They also exist in a $U(N)$ gauge theory with two $N$ by $N$ complex scalar fields coupled to each other. One non-Abelian sine-Gordon soliton can terminate on one non-Abelian global vortex. They are relevant in chiral Lagrangian of QCD or in color-flavor locked phase of high density QCD, where the anomaly is suppressed at asymptotically high temperature or density, respectively.
We study extremal and non-extremal generalizations of the regular non-abelian monopole solution of hep-th/9707176, interpreted in hep-th/0007018 as 5-branes wrapped on a shrinking S^2. Naively, the low energy dynamics is pure N=1 supersymmetric Yang-Mills. However, our results suggest that the scale of confinement and chiral symmetry breaking in the Yang-Mills theory actually coincides with the Hagedorn temperature of the little string theory. We find solutions with regular horizons and arbitrarily high Hawking temperature. Chiral symmetry is restored at high energy density, corresponding to l…
The percolation properties of equatorial strips of the two dimensional O(3) nonlinear $σ$ model are investigated numerically. Convincing evidence is found that a sufficently narrow strip does not percolate at arbitrarily low temperatures. Rigorous arguments are used to show that this result implies both the presence of a massless phase at low temperature and lack of asymptotic freedom in the massive continuum limit. A heuristic estimate of the transition temperature is given which is consistent with the numerical data.
We demonstrate that the application of any external uniform non-abelian gauge background, no matter how small, leads to a greatly enhanced degeneracy. This degeneracy is so large that even a non-abelian background field of infinitesimal strength leads to a shocking change in the thermodynamics. The critical temperature might be discontinuously depressed and an "avoided critical point" will emerge. Similar models were previously employed to describe the micropscopics of metallic glasses and correctly predicted the locations of the structure factor peaks. We will compare one of the fitted parame…
Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence. An analogous field theory calculation for free fermions, presented in the appendix, indicates our results may be a special feature of strong interactions.
We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number $Q \propto \int d^4x F_{μν}{\tilde F}^{μν}$, and show that it has a diffusive behaviour in the presence of an external magnetic field $B$. This indicates that the mechanism for fermionic num…
An expansion in the number of spatial covariant derivatives is carried out to compute the $ζ$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and imaginary parts of the Euclidean effective action are computed up to terms which are ultraviolet finite. The expansion used preserves gauge and parity symmetries and the correct multivaluation under large gauge transformations as well as the correct parity anomaly are reproduced. The result is shown to correctly reproduce known limiting cases, such as massless fe…
We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential $μ$ for the fermionic charge, and monitor its evolution with real-time classical lattice simulations. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemical potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral…
The most general two-dimensional dilaton gravity theory coupled to an Abelian gauge field is considered. It is shown that, up to spacetime diffeomorphisms and $U(1)$ gauge transformations, the field equations admit a two-parameter family of distinct, static solutions. For theories with black hole solutions, coordinate invariant expressions are found for the energy, charge, surface gravity, Hawking temperature and entropy of the black holes. The Hawking temperature is proportional to the surface gravity as expected, and both vanish in the case of extremal black holes in the generic theory. A Ha…
Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be formulated in terms of link variables which are subject to the Bianchi constraints. Using this representation we derive exact and local dual formulation for the partition function of such models on a cubic lattice in arbitrary dimension D. Locality means that the dual action is given by a sum over some subset of hypercubes of the dual lattice and the interaction between dual variables ranges over one given hypercube. Dual variables are in general discrete-valued and live on (D-2)-cell of the dual lattice, in close analogy…
Charged plasmas with chirality imbalance are unstable and tend to reduce the imbalance. This chiral plasma instability is, however, not captured in (anomalous) hydrodynamics for high-temperature non-Abelian plasmas. We derive a Langevin-type classical effective theory with anomalous parity-violating effects for non-Abelian plasmas that describes the chiral plasma instability at the magnetic scale. We show that the time scale of the instability is of order $[g^4 T \ln(1/g)]^{-1}$ at weak coupling.
Condensation of the Abelian monopoles and the center vortices leads to confinement of color in low temperature phase of Yang-Mills theory. We stress that these topological magnetic degrees of freedom are also very important in the deconfinement regime: at the point of the deconfinement phase transition both the monopoles and the vortices are released into the thermal vacuum contributing, in particular, to the equation of state and, definitely, to transport properties of the hot gluonic medium. Thus, we argue that a novel, magnetic component plays a crucial role. On the other hand, it was demon…
We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) lattice gauge theory. Using the Frohlich-Marchetti monopole creation operator we show numerically that the monopole condensate depends on the choice of the Abelian projection. Contrary to the claims in the current literature we observe that in the Abelian Polyakov gauge and in the field strength gauge the monopole condensate does not vanish at the critical temperature and thus is not an order parameter.
We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics theta=pi/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitude…
We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to $\mathcal{N}=4$ Super-Yang-Mills theory coupled to an $SU(2)$-current. All solutions are fully backreacted asymptotica…
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may …
We study the Debye mass, $m_D$, and the topological susceptibility, $χ$, at high temperatures in non-abelian gauge theory. Both exhibit, at some order in the perturbation expansion, infrared sensitivity. As a result, a perturbative analysis can at best provide an estimate of these quantities, subject to some uncertainty. The size of these uncertainties, particularly in the case of $χ$, has been the subject of some debate. For the perturbative free energy, reframing an analysis of Braaten and Pisarski, the estimate and the associated error, can be understood in terms of a {\it Wilsonian} effect…
In a holographic approach, the evolution of a 4D strongly coupled non-Abelian plasma towards equilibrium can be studied investigating a 5D gravitational dual. The process driving the plasma out-of-equilibrium can be described by boundary sourcing, a deformation of the boundary metric; the analysis of the late-time dynamics allows to understand how the hydrodynamic regime settles in. We apply the method to a boost-invariant case, considering the effects of different quenches, solving the Einstein equations in the bulk and studying the time-dependence of observables such as the effective tempera…
We discuss the effect of dynamical charged particles in U(1)^{N-1} Abelian effective theories of QCD. Screening and confinement at zero temperature are explained qualitatively. The effect of dynamically charged particle is expressed in terms of an effective action of integer electric currents. When a screening is expected, the static potential shows a flattening in the long-range region and a linear behavior in the intermediate region. We show why the screening is better observed in the Polyakov-loop correlators than in the Wilson loops. The breaking of the adjoint string is explained without …
We have developed the Hamiltonian theory for collective longitudinally polarized colorless excitations (plasmons) in a high-temperature gluon plasma using the general formalism for constructing the wave theory in nonlinear media with dispersion, which was developed by V.E. Zakharov. In this approach, we have explicitly obtained a special canonical transformation that makes it possible to simplify the Hamiltonian of interaction of soft gluon excitations and, hence, to derive a new effective Hamiltonian. The approach developed here is used for constructing a Boltzmann-type kinetic equation descr…
