Abstract
We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × \U0001d54a1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.
Highlights
This paper is about the connection between two recent developments in nonperturbative gauge theories which we find quite exciting and worthwhile.The first, more than a decade old, is the realization that complicated and analytically untractable problems in four-dimensional (4d) asymptotically free gauge theories — such as confinement and chiral symmetry breaking — yield to theoretically controlled analysis once spacetime is compactified to R3 × S1, where S1 is interpreted as a spatial circle and is not encoding finite temperature
Despite the expected matching of ’t Hooft anomalies, it is still interesting to give a detailed description thereof within the calculable R3 × S1 setup. Such a description entails1 determining how background fields gauging the global symmetries are coupled to the effective field theories (EFTs) that capture the dynamics at different scales
We expect that understanding the EFT’s coupling to global symmetry backgrounds will shed light on how various topological quantum field theories (TQFTs) appear in the deep IR, in a setup where the dynamics is understood at all scales
Summary
This paper is about the connection between two recent developments in nonperturbative gauge theories which we find quite exciting and worthwhile. Despite the expected matching of ’t Hooft anomalies, it is still interesting to give a detailed description thereof within the calculable R3 × S1 setup Such a description entails determining how background fields gauging the global symmetries are coupled to the EFTs that capture the dynamics at different scales. We expect that understanding the EFT’s coupling to global symmetry backgrounds will shed light on how various topological quantum field theories (TQFTs) appear in the deep IR, in a setup where the dynamics is understood at all scales Such IR TQFTs have been deemed necessary to match the new ’t Hooft anomalies, including anomaly inflow on the worldvolumes of domain walls. This already rather lengthy paper is entirely devoted to the first item above
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