Pin TQFT and Grassmann integral
| Autor: | Ryohei Kobayashi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Global Symmetries Nuclear and High Energy Physics Pure mathematics FOS: Physical sciences 01 natural sciences Mathematics::Algebraic Topology law.invention Condensed Matter - Strongly Correlated Electrons law 0103 physical sciences lcsh:Nuclear and particle physics. Atomic energy. Radioactivity Invariant (mathematics) 010306 general physics Spin-½ Physics Topological quantum field theory Strongly Correlated Electrons (cond-mat.str-el) 010308 nuclear & particles physics Topological States of Matter Partition function (mathematics) Mathematics::Geometric Topology Lattice (module) Invertible matrix High Energy Physics - Theory (hep-th) Grassmann integral Topological Field Theories lcsh:QC770-798 Anomaly (physics) |
| Zdroj: | Journal of High Energy Physics, Vol 2019, Iss 12, Pp 1-26 (2019) Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| Popis: | We discuss a recipe to produce a lattice construction of fermionic phases of matter on unoriented manifolds. This is performed by extending the construction of spin TQFT via the Grassmann integral proposed by Gaiotto and Kapustin, to the unoriented pin$_\pm$ case. As an application, we construct gapped boundaries for time-reversal-invariant Gu-Wen fermionic SPT phases. In addition, we provide a lattice definition of (1+1)d pin$_-$ invertible theory whose partition function is the Arf-Brown-Kervaire invariant, which generates the $\mathbb{Z}_8$ classification of (1+1)d topological superconductors. We also compute the indicator formula of $\mathbb{Z}_{16}$ valued time-reversal anomaly for (2+1)d pin$_+$ TQFT based on our construction. 26 pages, 6 figures |
| Databáze: | OpenAIRE |
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