The "Parity" Anomaly On An Unorientable Manifold
read the original abstract
The "parity" anomaly -- more accurately described as an anomaly in time-reversal or reflection symmetry -- arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. This anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold. In this paper, we give a full description of the "parity" anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions on a possibly unorientable spacetime. We consider an application to topological superconductors and another application to M-theory. The application to topological superconductors involves using knowledge of the "parity" anomaly as an ingredient in constructing gapped boundary states of these systems and in particular in gapping the boundary of a $\nu=16$ system in a topologically trivial fashion. The application to M-theory involves showing the consistency of the path integral of an M-theory membrane on a possibly unorientable worldvolume. In the past, this has been done only in the orientable case.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Extraordinary Surface Criticalities for Interacting Fermions
Exact infrared solutions for defect renormalization group flows in the 3D Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent topological and geometric structures in defect coup...
-
Extraordinary Surface Criticalities for Interacting Fermions
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
-
Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
-
Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions
Staggered fermions in 2+1d show modulo 8 parity/time-reversal anomalies that match between lattice and continuum when placed on tori and Klein bottles via a nontrivial symmetry map.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.