Lattice Analysis of SU(2) with 1 Adjoint Dirac Flavor

Abstract

Recently SU(2) gauge theory with one massless adjoint Dirac quark flavor emerges as a novel critical theory for the quantum phase transition between a trivial and a topological insulator in 3 + 1 dimensions. There are several classes of conjectured infrared dynamics for this theory. One possibility is that the theory undergoes spontaneous chiral symmetry breaking, with two massless Goldstone bosons (the scalar diquark and its antiparticle) in the infrared. Another scenario, which is suggested by previous lattice studies by Athenodorou et al., is that the IR sector of the theory is a strongly interacting conformal field theory as the quark mass vanishes. The most recent theoretical proposals argue for a case that in the infrared a composite fermion composed of two quarks and an antiquark becomes massless and non-interacting as the quark mass goes to zero, while other sectors are decoupled from this low-energy fermion. This work expands upon previous studies by including the composite fermion to investigate which of these three potential scenarios captures the infrared behavior of this theory.

Symmetries and strings of adjoint QCD2

“…There has been a lot of progress recently on some aspects of strongly coupled field theory dynamics, and, in particular, gauge theories with adjoint matter in 3 and 4 space-time dimensions. See for instance [2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

“…As a function of θ we have a first order transition at θ = π with two universes simultaneously having the lowest energy density. 12 12 We may compactify Euclidean time τ ∼ τ + β and compute the partition function as a function of R, β.…”