Tricritical points in a compactU(1)lattice gauge theory at strong coupling

Abstract

Pure compact U (1) lattice gauge theory exhibits a phase transition at gauge coupling g ∼ O(1) separating a familiar weak coupling Coulomb phase, having free massless photons, from a strong coupling phase. However, the phase transition was found to be of first order, ruling out any nontrivial theory resulting from a continuum limit from the strong coupling side. In this work, a compact U (1) lattice gauge theory is studied with addition of a dimension-two mass counterterm and a higher derivative (HD) term that ensures a unique vacuum and produces a covariant gauge-fixing term in the naive continuum limit. For a reasonably large coefficient of the HD term, now there exists a continuous transition from a regular ordered phase to a spatially modulated ordered phase. For weak gauge couplings, a continuum limit from the regular ordered phase results in a familiar theory consisting of free massless photons. For strong gauge couplings with g ≥ O(1), this transition changes from first order to continuous as the coefficient of the HD term is increased, resulting in tricritical points which appear to be a candidate in this theory for a possible nontrivial continuum limit.

Non-perturbatively gauge-fixed compact U(1) lattice gauge theory

“…In this paper, continuing our work from before [1,20], we present results from our numerical simulations of nonperturbative gauge-fixing for the abelian case as proposed in [6,7]. Our work on the non-abelian case involving eBRST formalism is in progress and will be reported elsewhere.…”

“…Only recently, as mentioned in [1], we have realised the limitations of the configurationgenerating algorithm, multihit Metropolis (MM), used in all earlier studies in the weak gauge coupling region [21] and also in the earlier work at strong coupling [20]. As we shall see in the next Section, the HD gauge-fixing term involves the square of the gauge-covariant lattice laplacian, and as a result the action density at a lattice site involves significantly more lattice links than the usual Wilson plaquette.…”

“…For Yang-Mills theories on a discrete space-time euclidean lattice, Wilson in his seminal paper [8] introduced a manifestly gauge-invariant formalism, that works equally well for abelian theories, in terms of a functional integral with a gauge-invariant Haar measure using group-valued fields on the links of the lattice (so that the algebra-valued gauge fields are compact). For vector-like theories like QCD and QED, where gauge-invariance can be maintained on the regulator, Wilson's gauge-invariant scheme is highly successful, although gauge-fixing may be necessary for matching to a perturbative renormalisation scheme like M S. However, given that fermions on the lattice needs to explicitly break chiral symmetry [9][10][11][12], for chiral gauge theories gauge-invariance is broken on the lattice regulator 1 . In a manifestly local formalism of lattice chiral gauge theories, the standard Wilson method with a gauge-invariant measure leads to various problems [14,15].…”

“…In [1], results of the phase diagram and the emerging physics at the continuous part of the FM-FMD transition obtained with the newly employed HMC algorithm for the HD action were presented only at one value of the strong gauge coupling, viz., g = 1.3. The current work aims at a consistent and comprehensive picture applicable in general for a wide range of parameters to determine especially how the strong gauge coupling phase diagram gradually emerges from that of the weak gauge coupling region and how the two regions are related, if at all.…”

Non-perturbative gauge-fixing

“…Our work [2,3,4] focusses on two non-perturbative gauge-fixing proposals, one for U(1) theory and the other for SU(N) gauge theories, and numerically investigate them.…”