{"work":{"id":"5ea2b3b8-e834-4b00-9d94-1afde8264331","openalex_id":null,"doi":null,"arxiv_id":"1703.00501","raw_key":null,"title":"Theta, Time Reversal, and Temperature","authors":null,"authors_text":"D","year":2017,"venue":"hep-th","abstract":"$SU(N)$ gauge theory is time reversal invariant at $\\theta=0$ and $\\theta=\\pi$. We show that at $\\theta=\\pi$ 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 $\\theta=\\pi$ the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at $\\theta=0$ 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 $\\theta=\\pi$, 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 $\\theta=\\pi$ 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 $\\theta=\\pi$ is gapless, e.g. a Coulomb phase could match the underlying anomalies.","external_url":"https://arxiv.org/abs/1703.00501","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T05:50:23.803980+00:00","pith_arxiv_id":"1703.00501","created_at":"2026-05-10T14:05:30.028292+00:00","updated_at":"2026-06-05T21:23:00.469572+00:00","title_quality_ok":false,"display_title":"Theta, Time Reversal, and Temperature","render_title":"Theta, Time Reversal, and Temperature"},"hub":{"state":{"work_id":"5ea2b3b8-e834-4b00-9d94-1afde8264331","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":18,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2022-05-19T13:15:29+00:00","last_pith_cited_at":"2026-05-21T18:00:32+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-06T18:11:04.229056+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":12}],"polarity_counts":[{"context_polarity":"background","n":12}],"runs":{},"summary":{},"graph":{},"authors":[]}}