Generalized ’t Hooft anomalies on non-spin manifolds

Self Cite

We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × 𝕊1 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.

Section: Nmentioning

confidence: 81%

Section: Nmentioning

confidence: 99%

See 1 more Smart Citation

Topological terms and anomaly matching in effective field theories on ℝ3 × 𝕊1. Part I. Abelian symmetries and intermediate scales

Poppitz

Wandler

2021

Self Cite

“…When we put the theory on non-spin manifolds, such as CP 2 , by introducing a kind of spin-charge relation, we can obtain stronger constraints from center-chiral mixed anomaly [69]. The index of Dirac operators on CP 2 with minimal non-trivial 't Hooft flux turns out to be (1 + N/2) mod N , if we do not introduce any flux on U(1)/ZN for even N .…”

Section: Generalized 'T Hooft Anomaly For θ Periodicitymentioning

confidence: 99%

Universality between vector-like and chiral quiver gauge theories: anomalies and domain walls

Sulejmanpašić

Tanizaki

Ünsal

2020

We study low-energy dynamics of [SU(N)] K chiral quiver gauge theories in connection with N = 1 super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by Z K orbifold projections of N = 1 SU(N K) SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for K ≥ 3. In order to study low-energy behaviors, we analyze these systems using 't Hooft anomaly matching and reliable semiclassics on R 3 × S 1. Thanks to 't Hooft anomaly that involves 1-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist N vacua. Theories with even K possess a physical θ angle despite the presence of massless fermions, and we further predict the N-branch structure associated with it; the number of vacua is enhanced to 2N at θ = π due to spontaneous CP breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on R 3 × S 1 with the double-trace deformation. Symmetry and anomaly of odd-K theories are the same as those of the N = 1 SYM, and the ones of even-K theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.

“…This anomaly was further enlarged in [25] by considering the most general fractional charges in the baryon number, color, and flavor (BCF) directions. This anomaly was dubbed the BCF anomaly (or only BC anomaly when we have a single flavor), and was also studied in [26] on nonspin manifolds. One of the profound consequences of the BCF anomaly is the deconfinement of quarks on axion…”

Section: Introductionmentioning

confidence: 99%

Condensates and anomaly cascade in vector-like theories

Anber

2021

Self Cite

We study the bilinear and higher-order fermion condensates in 4-dimensional SU(N) gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the 0-form discrete chiral, 1-form center, and 0-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with 2-index (anti)symmetric fermions. We also contrast the BC anomaly with the 0-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the 0-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the 1-form center symmetry in order to match the BC anomaly, while the 0-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is 2-dimensional. We show that the BC anomaly cascades from 4 to 2 dimensions.