Parity and Spin CFT with boundaries and defects

Ingo Runkel; Lóránt Szegedy; Gérard M. T. Watts

doi:10.48550/arXiv.2210.01057

Parity and Spin CFT with boundaries and defects

Ingo Runkel, Lóránt Szegedy, Gérard M. T. Watts

Research output: Working paper/Preprint › Preprint

6 Citations (Scopus)

107 Downloads (Pure)

Abstract

This paper is a follow-up to [82] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [45] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra F in a suitable ribbon fusion category, such that the Nakayama automorphism of F is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of F and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a Z ₂-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.

Original language	English
Publisher	SciPost
Volume	15
DOIs	https://doi.org/10.48550/arXiv.2210.01057 https://doi.org/10.21468/SciPostPhys.15.5.207
Publication status	Published - 27 Nov 2023

Publication series

Name	SciPost Physics

Keywords

hep-th
math-ph
math.MP
math.QA

Access to Document

2210.01057v1

Cite this

@techreport{51588dfb4037438d8fc49353eb9f9a27,

title = "Parity and Spin CFT with boundaries and defects",

abstract = "This paper is a follow-up to [82] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [45] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra F in a suitable ribbon fusion category, such that the Nakayama automorphism of F is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of F and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a Z 2-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.",

keywords = "hep-th, math-ph, math.MP, math.QA",

author = "Ingo Runkel and L{\'o}r{\'a}nt Szegedy and Watts, {G{\'e}rard M. T.}",

note = "Funding Information: IR is partially supported by the Deutsche Forschungsgemeinschaft via the Cluster of Excellence EXC 2121 “Quantum Universe” - 390833306. LS is supported by the Walter Benjamin Fellowship of the Deutsche Forschungsgemeinschaft. Funding Information: Funding information IR is grateful to King{\textquoteright}s College London for hospitality during the summer term 2022, and to the Aspen Center for Physics for a 2-week stay supported by National Science Foundation grant PHY-1607611. LS is grateful to King{\textquoteright}s College London for hospitality and support during the week of the Defects and Symmetry meeting in Summer 2022. Publisher Copyright: Copyright I. Runkel et al.",

year = "2023",

month = nov,

day = "27",

doi = "10.48550/arXiv.2210.01057",

language = "English",

volume = "15",

series = "SciPost Physics",

publisher = "SciPost",

edition = "5",

type = "WorkingPaper",

institution = "SciPost",

}

TY - UNPB

T1 - Parity and Spin CFT with boundaries and defects

AU - Runkel, Ingo

AU - Szegedy, Lóránt

AU - Watts, Gérard M. T.

N1 - Funding Information: IR is partially supported by the Deutsche Forschungsgemeinschaft via the Cluster of Excellence EXC 2121 “Quantum Universe” - 390833306. LS is supported by the Walter Benjamin Fellowship of the Deutsche Forschungsgemeinschaft. Funding Information: Funding information IR is grateful to King’s College London for hospitality during the summer term 2022, and to the Aspen Center for Physics for a 2-week stay supported by National Science Foundation grant PHY-1607611. LS is grateful to King’s College London for hospitality and support during the week of the Defects and Symmetry meeting in Summer 2022. Publisher Copyright: Copyright I. Runkel et al.

PY - 2023/11/27

Y1 - 2023/11/27

N2 - This paper is a follow-up to [82] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [45] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra F in a suitable ribbon fusion category, such that the Nakayama automorphism of F is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of F and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a Z 2-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.

AB - This paper is a follow-up to [82] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [45] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra F in a suitable ribbon fusion category, such that the Nakayama automorphism of F is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of F and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a Z 2-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.

KW - hep-th

KW - math-ph

KW - math.MP

KW - math.QA

UR - http://www.scopus.com/inward/record.url?scp=85178122407&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2210.01057

DO - 10.48550/arXiv.2210.01057

M3 - Preprint

VL - 15

T3 - SciPost Physics

BT - Parity and Spin CFT with boundaries and defects

PB - SciPost

ER -

Parity and Spin CFT with boundaries and defects

Abstract

Publication series

Keywords

Access to Document

Other files and links

Fingerprint

Cite this