Conformal field theory and the hot phase of three-dimensional U(1) gauge theory

Abstract

We study the high-temperature phase of compact U(1) gauge theory in 2 + 1 dimensions, comparing the results of lattice calculations with analytical predictions from the conformalfield-theory description of the low-temperature phase of the bidimensional XY model. We focus on the two-point correlation functions of probe charges and the field-strength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory. arXiv:1903.00491v2 [cond-mat.str-el] 13 May 2019Polyakov loop can be directly related to the free energy associated with a chromoelectric probe charge: in the thermodynamic limit P vanishes for T < T c (implying an infinite energy cost for the existence of an isolated fundamental color source in the confining phase, i.e. quark confinement), whereas it has a finite expectation value at T > T c . In contrast, the U(1) center symmetry of U(1) gauge theory in 2 + 1 dimensions remains unbroken, and, while in the high-temperature phase the theory does not have a dynamically generated, finite, characteristic length scale, the logarithmic Coulomb potential is still sufficient to confine static charges.As the finite-temperature transition in U(1) gauge theory in 2 + 1 dimensions is continuous, one expects that at T = T c the long-distance properties of the system are equivalent to those of a two-dimensional spin system with global U(1) symmetry [116], i.e. the classical XY model, that exhibits a Kosterlitz-Thouless transition [117] (see also refs. [118-121]). In the past, the validity of this conjecture has been investigated in various numerical studies [87,[101][102][103] and the most recent work gives conclusive evidence in support of it [104].As discussed in ref. [116], this correspondence relies on the continuous nature of the transition at T = T c . In turn, the existence of an infinite correlation length is also an essential necessary condition for scale and conformal invariance. In the two-dimensional XY model, this condition is realized in a peculiar way: even though the system can never have spontaneous magnetization [122], at low temperatures the model is in a phase characterized by "topological" order [117], with two-point spin correlation functions decaying only with inverse powers of the spatial separation r between the spins [123,124]. The fact that the whole low-temperature phase of the two-dimensional XY model is gapless and admits a conformal-field-theory description raises the question, what happens in the corresponding phase of the three-dimensional gauge theory, i.e. the high-temperature phase? To answer this question, in this work we carry out a systematic study of compact U(1) lattice gauge theory at T > T c , and compare a large set of novel numerical results, obtained by Monte Carlo simulations, with analytical predictions derived from conformal field theory. Specifically, we focus our attention on correlation functions of plaquette operators, Polyakov loops, and on the profile of the flux tube ind...

Effective String Description of the Confining Flux Tube at Finite Temperature

“…The fact that this shift is so small is another evidence of the goodness of the Nambu-Goto approximation. It is interesting to notice that this agreement holds for all the LGTs which have been studied [58][59][60][61][62], both in (2 + 1) and in (3 + 1) dimensions, with the only exception of the 3D U(1) model [63], for which, in fact, a different EST is expected [8,64], with a dominant contribution from the extrinsic curvature term.…”

“…The major difference between the two ESTs is in the shape and width of the flux tube [9]. Interestingly this difference is magnified exactly in the high temperature regime [9,64] which is the subject of this review. It would be interesting to pursue this study to better understand the role of the extrinsic curvature term in driving this difference and, more importantly, which one better describes the behaviour of the flux tube in non-abelian LGTs.…”

Topological defects and confinement with machine learning: The case of monopoles in compact electrodynamics

“…We calculate numerically the vacuum expectation value (14) of the Polyakov loop (13) at a dense set of lattice gauge couplings β and fit the result by the following function:…”

“…The goal is to extract the critical temperature of the phase transition from the predictions. Therefore, we focus on the most relevant quantities for this purpose: the absolute value of the Polyakov loop L (order parameter) defined in (14) (we omit the symbol h•i) and the phase label:…”

“…Contrary to the theory of strong interactions, the nonperturbative effects in cQED are well understood. The confinement and mass gap generation admit an analytical treatment in a weak coupling regime of zero-temperature cQED [1], while the phase transition may be characterized both by analytical and numerical techniques [9][10][11][12][13][14]. In the context of Abelian theory, the dynamics of the Abelian monopoles can explain all these nonperturbative phenomena.…”