We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as $L^3$.
We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.
The charge screening, confinement of fermion quantum numbers and the chiral condensate formation in two-dimensional QED is studied in details. It is shown that charge screening and confinement of fermion number in two-dimensional QED is due to an appearance of gauge fields which nullify the Dirac determinant. An appearance of the fields of another type but with the same property yield the chiral condensate formation. In addition, these second type fields ensure the "softness" of the charge screening in a process which is analogous to the $e^+e^-$ annihilation.
A generalization of Born-Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces, in the limit as b0 tends to infinity, to Maxwell's linear vacuum theory while for finite b0 it reduces to the original Born-Infeld model. The spherically symmetric static sector of the theory is explored in a backgro…
We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient $θ$ reaches a critical value which depends upon the number…
Recently, there has been much interest in simulating quantum field theory effects of matter and gauge fields. In a recent work [Phys. Rev. Lett. 107, 275301 (2011)] a method for simulating compact Quantum Electrodynamics (cQED) using Bose-Einstein condensates has been suggested. We suggest an alternative approach, which relies on single atoms in an optical lattice, carrying 2l+1 internal levels, which converges rapidly to cQED as l increases. That enables the simulation of cQED in 2+1 dimensions in both the weak and the strong coupling regimes, hence allowing to probe confinement as well as ot…
Compact quantum electrodynamics in 2+1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when $N>N_c=36/π^3\approx 1.161$, where $N$ is the number of fermion replica. For $N<N_c$, however, there are two stable fixed points separated by a line containing a unstable non-trivial fixed point: a fixed point corresponding to the scaling limit…
Institut Denis Poisson CNRS/UMR 7013（丹尼斯·泊松研究所（法国国家科学研究中心/7013联合研究单位））；Université de Tours（图尔大学）；Pacific Quantum Center（太平洋量子中心）；Far Eastern Federal University（远东联邦大学）；Dipartimento di Fisica, Universitá di Torino（都灵大学物理系）；INFN Sezione di Torino（意大利国家核物理研究所都灵分所）；Arnold-Regge Center（阿诺德-雷格中心）
We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning …
We argue that the effective theory for electromagnetic fields in spatially varying meson condensations in dense nuclear and quark matter is given by the axion electrodynamics. We show that one of the helicity states of photons there has the nonrelativistic gapless dispersion relation $ω\sim k^2$ at small momentum, while the other is gapped. This "nonrelativistic photon" may also be realized at the interface between topological and trivial insulators in condensed matter systems.
Features of screening and confinement are reviewed in two-dimensional quantum electrodynamics (QED2). Our discussion is carried out using the gauge-invariant but path-dependent variables formalism. This alternative and useful approach exploits the rich structure of the electromagnetic cloud or dressing around static fermions in a straightforward and simple way.
We show that the four-dimensional U(1) gauge theory in the continuum formulation has a confining phase (exhibiting area law of the Wilson loop) in the strong coupling region above a critical coupling $g_c$. This result is obtained by taking into account topological non-trivial sectors in U(1) gauge theory. The derivation is based on the reformulation of gauge theory as a deformation of a topological quantum field theory and subsequent dimensional reduction of the D-dimensional topological quantum field theory to the (D-2)-dimensional nonlinear sigma model. The topological quantum field theory …
Three-dimensional gapless semiconductors with quadratic band touching, such as HgTe, $α$-Sn, or Pr$_2$Ir$_2$O$_7$ are believed to display a non-Fermi-liquid ground state due to long-range electron-electron interaction. We argue that this state is inherently unstable towards spontaneous formation of a (topological) excitonic insulator. The instability can be parameterized by a critical fermion number $N_c$. For $N < N_c$ the rotational symmetry is spontaneously broken, the system develops a gap in the spectrum, and features a finite nematic order parameter. To leading order in the 1/N expansion…
Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi liquid behavior, and also has wide applications in condensed matter physics. We study the effects of random potentials, which exist in almost all realistic condensed-matter systems, on the low-energy behaviors of massless Dirac fermions by means of renormalization group method, and show that the role of random mass is significantly enhanced by the gauge interaction, whereas random scalar and vector potentials are insusceptible to the…
Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently-reported quantum oscillations of the thermal conductivity in the field-induced quantum pa…
We explore the physical consequences of a new nonlinear electrodynamics, for which the electric field of a point-like charge is finite at the origin, as in the well-known Born-Infeld electrodynamics. However, contrary to the latter, in this new electrodynamics the phenomenon of birefringence and dichroism take place in the presence of external magnetic fields. Subsequently we study the interaction energy, within the framework of the gauge-invariant but path-dependent variables formalism. Interestingly enough, the static potential profile contains a linear potential leading to the confinement o…
In this paper we discuss well-known three- and two-dimensional models with confinement, namely, the Polyakov compact electrodynamics in 3D and two-dimensional CP(N-1) sigma model, and reveal changes in the confining regimes of these model upon adding the axion field. In both cases the addition of axion has a drastic impact. In the CP(N-1) model the axion-induced deconfinement was known previously, but we discuss a new feature not considered in the previous publication.
Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$ dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These systems also exhibit the spontaneous breaking of higher-form $\mathbb{Z}_k$ symmetries and topological orders for level $k \geq 2$. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level $k$ in $(3+1)$ dimensions in background fields that hosts both gapped and gapless modes. We argu…
Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics (or axionic electrodynamics in the presence of a minimal length). Accordingly, we obtain an ultraviolet finite static potential which is the sum of a Yukawa-type and a linear potential, leading to the confinement of static charges. Interestingly, it should be noted that this calculation involves no theta expansion at all. The present result makes manifest the key role played by the new quantum of length in our analysis.
We briefly outline several main results concerning various new physically relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$ gravity in the first-order formalism, coupled to a special kind of nonlinear electrodynamics containing a square-root of the standard Maxwell Lagrangian and known to produce charge confinement in flat spacetime.
In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. This theory is quite important to investigate the phase structures of QED$_3$ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the t-J model of high-temperature superconductivity. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of…
We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum anti-ferromagnets. In the presence of $\mathbb{Z}_2$ preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the Valence Bond Solid (VBS) phase of quantum magnets. We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is…
We argue that the compact three dimensional electrodynamics with massless fermions is always confining, in spite of the bare interaction between the magnetic monopoles being rendered logarithmic by fermions. The effect is caused by screening by other dipoles, which transforms the logarithmic back into the Coulomb interaction at large distances. Possible implications for the chiral symmetry breaking for fermions are discussed, and the global phase diagram of the theory is proposed.
Quantum electrodynamics in three spacetime dimensions, with one massless fermion species, is studied using a non-perturbative variational approach. Quantization of the theory follows Dirac's Hamiltonian procedure, with a gauge invariant factorization of the physical degrees of freedom. Due to pair condensation in the vacuum state, the symmetry of parity is spontaneously broken. As a consequence, fermionic quasi-particles propagating in the condensate can be identified and are seen to possess a confining dynamical mass, while the propagating physical electromagnetic mode also acquires a non-van…
The compact U(1) gauge field occurs in many fractionalized descriptions of low dimensional quantum magnetism and heavy fermion systems. In this respect a fundamental question about the gauge field is whether it is confined or not in the presence of Fermi surface. In this paper we show that the U(1) gauge field with a possible positive anomalous dimension in the presence of Fermi surface has to be in the confined state, although it is strongly coupled to abundant gapless fermionic excitations near the Fermi surface in two spatial dimensions. This means that some quantum spin liquids and/or frac…
We propose a method for simulating 2+1-d compact lattice quantum-electrodynamics (QED), using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates' phases correspond to the electromagnetic vector-potential, and the fluctuations of the local number operators represent the conjugate electric field. The gauge invariant Kogut-Susskind Hamiltonian is obtained as an effective low energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to 'electric flux-tubes' and to confinement. The effect can be obse…
The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of $N_f$ flavors of interacting Dirac fermions charged under a U(1) gauge field in 2+1 dimensions. Using Quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfin…
We argue that, at finite temperature, parity invariant non-compact electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We show that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integral multiple of the electron charge. The effective field theory for the Polyakov loop operator is a 2-dimensional Euclidean scalar field theory with a global discrete symmetry $Z$, the additive group of the integers. We argue that the re…
We analyse dependence of the partition function on the boundary condition for the longitudinal component of the electric field strength in gauge field theories. In a physical gauge the Gauss law constraint may be resolved explicitly expressing this component via an integral of the physical transversal variables. In particular, we study quantum electrodynamics with an external charge and SU(2) gluodynamics. We find that only a charge distribution slowly decreasing at spatial infinity can produce a nontrivial dependence in the Abelian theory. However, in gluodynamics for temperatures below some …
The ground state of quantum chromodynamics in sufficiently strong external magnetic fields and at moderate baryon chemical potential is a chiral soliton lattice (CSL) of neutral pions. We investigate the interplay between the CSL structure and dynamical electromagnetic fields. Our main result is that in presence of the CSL background, the two physical photon polarizations and the neutral pion mix, giving rise to two gapped excitations and one gapless mode with a nonrelativistic dispersion relation. The nature of this mode depends on the direction of its propagation, interpolating between a cir…
Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a linear raise of the potential between particles with opposite electric charges at sufficiently large inter-particle separation. The confinement is generated by condensation of Abelian monopoles at strong gauge coupling. We study the properties of monopoles and the deconfining order parameter in zero-temperature theory in the presence of ideally conducting parallel metallic boundaries (plates) usually associated with the Casimir effect. Using first-principle numerical simulations in compact U(1) lattic…
Alice electrodynamics (AED) is a theory of electrodynamics in which charge conjugation is a local gauge symmetry. In this paper we investigate a charge instability in alice electrodynamics in (2+1)-dimensions due to this local charge conjugation. The instability manifests itself through the creation of a pair of alice fluxes. The final state is one in which the charge is completely delocalized, i.e., it is carried as cheshire charge by the flux pair that gets infinitely separated. We determine the decay rate in terms of the parameters of the model. The relation of this phenomenon with other sa…
The vacuum of supersymmetric gauge theories (SQCD) with N=2 softly broken to N=1 resembles that of a BCS superconductor in that it has a condensate which collimates flux into vortices, leading to confinement. We embed the SQCD vortex into the BCS theory by identifying the N=1 vector multiplet mass and lightest massive chiral multiplet mass with the Fermi velocity divided by the London penetration depth and coherence length respectively. Thus embedded the superconductivity is type I and so the vortex core is smaller than the coherence length. Therefore nonlocal effects (Pippard electrodynamics)…
A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple an…
U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. The naturally chosen correlation functions converge to the correlation functions of the R-gauge electrodynamics on three- and four-dimensional torus as the lattice spacing approaches zero only for the special scaling. This special scaling depends on a choice of a correlation function system. Another scalings give the degenerate continuum limits. The Wilson criterion for the confinement is ambiguous. The asymptotics of the smeared Wilson loop integral for the large loop…
$\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on $\mathbb{R}^3\times S^1$ is believed to have a smooth dependence on the circle size $L$. Making $L$ small leads to calculable non-perturbative color confinement, mass gap, and string tensions. For finite $N$, the small-$L$ low-energy dynamics is described by a three-dimensional effective theory. The large-$N$ limit, however, reveals surprises: the infrared dual description is in terms of a theory with an emergent fourth dimension, curiously reminiscent of T-duality in string theory. Here, however, the emergent dimension is a lattice, with mome…
Discussions are made on the relationship between physical states and gauge independence in QED. As the first candidate take the LSZ-asymptotic states in a covariant canonical formalism to investigate gauge independence of the (Belinfante's) symmetric energy-momentum tensor. It is shown that expectation values of the energy-momentum tensor in terms of those asymptotic states are gauge independent to all orders. Second, consider gauge invariant operators of electron or photon, such as the Dirac's electron or Steinmann's covariant approach, expecting a gauge invariant result without any restricti…
We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED$_3$ and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.
Using a one-loop renormalization group improvement for the effective potential in the Higgs model of electrodynamics with electrically and magnetically charged scalar fields, we argue for the existence of a triple (critical) point in the phase diagram ($λ_{run}, g_{run}^4$), where $λ_{run}$ is the renormalised running selfinteraction constant of the Higgs scalar monopoles and $g_{run}$ is their running magnetic charge. This triple point is a boundary point of three first-order phase transitions in the dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two confinement phases mee…
We consider three dimensional quantum electrodynamics (cQED3) with massless relativistic fermions coupled to a compact gauge field using a combined perturbative variational approach. Coupling to matter renders the bare interaction between magnetic monopoles logarithmic at large distances, suggesting the possibility of a confinement-deconfinement transition of the Berezinskii-Kosterlitz-Thouless type in the theory. Our self-consistent calculation suggests, however, that screening effects always destabilise the confined phase, in agreement with the previous renormalisation group study of the sam…
The path integral for 3+1 abelian gauge theory is rewritten in terms of a real antisymmetric field allowing a dual action that couples the electric and magnetic currents to the photon and each other in a gauge invariant manner. Standard perturbative abelian quantum electrodynamics reemerges when the monopole current vanishes. For certain simple relationships between the monopole current and the electric current, the altered photon propagator can exhibit abelian charge confinement or develop mass, modeling effects believed to be present in non-abelian theories.
In this paper we study a 3D lattice spin model of CP$^1$ Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of CP$^1$ bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) (O(4)) spin model with long-range and/or multi-spin interactions. It is also closely related to the recently proposed "Ginzburg-Landau" theory for quantum phase transitions of $s=1/2$ quantum spin systems on a 2D square lattice at zero temperature. We numerically study the phase structure of the model by…
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.
We examine the possibility of a confinement-deconfinement phase transition at finite temperature in both parity invariant and topologically massive three-dimensional quantum electrodynamics. We review an argument showing that the Abelian version of the Polyakov loop operator is an order parameter for confinement, even in the presence of dynamical electrons. We show that, in the parity invariant case, where the tree-level Coulomb potential is logarithmic, there is a Berezinskii-Kosterlitz-Thouless transition at a critical temperature ($T_c=e^2/8π+{\cal O}(e^4/m)$, when the ratio of the electrom…
