Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Abstract

This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete 't Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete 't Hooft anomaly matching to theories on R 2 and its compactification to R × S 1 L . We then compare the 't Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are N q vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e iθ/N q , which provides the N q-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by "quantum" instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-N limit of the Schwinger model with twisted boundary conditions satisfy volume independence. arXiv:1905.05781v3 [hep-th]

Undoing decomposition

“…In passing, it is also worth mentioning that gauging the flavor symmetry in these models can also be of interest, see [41, section 2.4] and [42][43][44].…”

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow

“…The mixed 0-form/1form anomalies imply that in theories with such anomalies, DWs occurring due to 0-form discrete symmetry breaking have a nontrivial structure on their worldvolume. Such DWs have recently received some attention [27][28][29][30][31][32][33][34][35][36]. The nontrivial DW physics is usually described in terms of a topological quantum field theory (TQFT) living on the DW, e.g.…”

Self-conjugate QCD

“…There has been only a few studies, see [20,22,[35][36][37], that attempted to combine both methods, 't Hooft anomalies and compactification, to maximize our learning about strongly coupled theories. The purpose of this work is to further examine the interplay between both methods and use them to shed light on gauge theories endowed with fermions in the self-conjugate representations.…”

“…Furthermore, we express the roots and weights in the R N basis. 20 Then, it is a simple exercise to show that the global minima of V (σ) in the fundamental domain are given by The dual photon masses are given by…”

“…Recently, it has been realized that in addition to the anomalies of the 0-form symmetries, which act on local fields, one may turn on background gauge fields of higher-form symmetries [2]. The obstruction to gauging these symmetries, hence higher-form 't Hooft anomalies [3], work as additional constraints on the possible realizations of the IR dynamics, see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] for recent advances.…”