Theta, time reversal and temperature
By D. Gaiotto, A. Kapustin, Z. Komargodski, N. Seiberg. 2017
382 citations recorded by the source corpus.
A bstractSU(N ) gauge theory is time reversal invariant at θ = 0 and θ = π. We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ = π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ = 0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at θ = π, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at θ = π is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O(2)-symmetric fixed points. It may also be that the four-dimensional theory around θ = π is gapless, e.g. a Coulomb phase could match the underlying anomalies.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/56adf5e89725c605370df8f8819518f8a4c4507c
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In Nuclear and High Energy Physics
Citations in the corpus
- On finite symmetries and their gauging in two dimensions (2017, methodology): “We write down basic sets of linear maps between (tensor products of) Hilbert spaces on S(1) and basic 2Recently in [5], Gaiotto, Kapustin, Komargodski and Seiberg performed an impressive study of the phase structure of thermal 4d su(2) Yang-Mills theory.”
- Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “In terms of anomalies one may derive the degeneracy at θ “ π, following [23], by noting that for this value of θ, there is a mixed anomaly between Up1q and C and hence a unique ground state is forbidden.”
- Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions (2017, neutral): “(For low values of N , especially for N = 2, there are also other plausible scenarios [6].”
- Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, result): “This discussion is analogous to a similar example in [66].”
- Comments on one-form global symmetries and their gauging in 3d and 4d (2018, methodology): “(For small values of N there are also other logical options [2].”
- On gauging finite subgroups (2017, methodology): “Here we stick to pure formalities and give a derivation, essentially the one given in Appendix B of [9].”