### Abstract

The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details - in particular the global moduli/instanton/magnetic charge structure - have remained elusive. Here we deduce from anomaly cancellation a natural candidate for the holographic dual of this nonabelian 2-form field, under AdS_{7}/CFT_{6} duality. We find this way a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

Original language | English (US) |
---|---|

Pages (from-to) | 229-321 |

Number of pages | 93 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2014 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)

### Cite this

*Advances in Theoretical and Mathematical Physics*,

*18*(2), 229-321. https://doi.org/10.4310/ATMP.2014.v18.n2.a1

**Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory.** / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Article

*Advances in Theoretical and Mathematical Physics*, vol. 18, no. 2, pp. 229-321. https://doi.org/10.4310/ATMP.2014.v18.n2.a1

}

TY - JOUR

T1 - Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory

AU - Fiorenza, Domenico

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details - in particular the global moduli/instanton/magnetic charge structure - have remained elusive. Here we deduce from anomaly cancellation a natural candidate for the holographic dual of this nonabelian 2-form field, under AdS7/CFT6 duality. We find this way a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

AB - The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details - in particular the global moduli/instanton/magnetic charge structure - have remained elusive. Here we deduce from anomaly cancellation a natural candidate for the holographic dual of this nonabelian 2-form field, under AdS7/CFT6 duality. We find this way a 7-dimensional nonabelian Chern-Simons theory of String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in an affine Kac-Moody Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

UR - http://www.scopus.com/inward/record.url?scp=84921267526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921267526&partnerID=8YFLogxK

U2 - 10.4310/ATMP.2014.v18.n2.a1

DO - 10.4310/ATMP.2014.v18.n2.a1

M3 - Article

AN - SCOPUS:84921267526

VL - 18

SP - 229

EP - 321

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 2

ER -