Domain wall moduli in softly-broken SQCD at θ¯=π

Abstract

We analyze the moduli space dynamics of domain walls in SUðNÞ QCD atθ ¼ π, by softly breaking N ¼ 1 SQCD with sfermion mixing. In the supersymmetric limit, BPS domain walls between neighboring vacua are known to possess nontranslational flavor moduli that form a CP N−1 sigma model. For the simplest case with gauge group SUð2Þ and N f ¼ 2, we show that this sigma model also exhibits a Hopf term descending from the bulk Wess-Zumino term with a quantized coefficient. On soft-breaking of supersymmetry via sfermion mixing that preserves the flavor symmetry, these walls and their moduli-space dynamics survives whenθ ¼ π so that there are two degenerate vacua.

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

“…General discrete anomaly inflow arguments and the 3 To avoid confusion, we stress that the total magnetic flux carried along a DW is zero. 4 There is a vast literature on various aspects of DWs in SYM; an incomplete list is [29,30,39,[41][42][43][44][45]. 5 See the main text for a detailed explanation.…”

“…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.…”

“…stretching between W p and W p+k(modN ) , is called a "k-wall." The physics of the DWs in SYM theory is quite rich and has been the subject of many investigations over the past 20 years, for example [29,30,37,[39][40][41][42][43][44][45]. 14…”

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)

“…The constant field strength background we use here to motivate the flux quantization (2.18) (and (2.24) below) is an example of configurations obeying the twisted boundary conditions discussed in the Appendix, see (C.12). 12 We denote the gauge field in these flux backgrounds A i (here and below i = 1, 2, 12 = 1) and take…”

“…Fortunately enough, DW are amenable to perturbative analysis at T T c , which makes them excellent objects to study compared to their low-temperature counterparts, the center vortices. 2 Despite the fact that DW in Yang-Mills theory are well studied in the literature, in the perturbative regime [3][4][5][6][7][8][9][10][11][12], on the lattice [13,14], via holography [8,10,15,16], or with an emphasis on DW in supersymmetric Yang-Mills theory [17][18][19][20][21][22], the DW worldvolume theory and the interplay between the bulk and DW physics remain, in many cases, a largely unexplored territory. 3 A renewed impetus for such studies is provided by the recent realization that DW must have rich worldvolume dynamics, required by newly discovered anomalies [2,23,24], as discussed further below.…”