### Abstract

We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus Tn(n≥2), by a noncommutative Tn-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a Z2-symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case.

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

Pages (from-to) | 240-251 |

Number of pages | 12 |

Journal | Journal of Geometry and Physics |

Volume | 92 |

DOIs | |

State | Published - Jun 1 2015 |

### Fingerprint

### Keywords

- Higher abelian gauge theory
- Noncommutative torus
- S-duality
- Strict deformation quantization
- String theory

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

### Cite this

**Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality.** / Mathai, Varghese; Sati, Hisham.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality

AU - Mathai, Varghese

AU - Sati, Hisham

PY - 2015/6/1

Y1 - 2015/6/1

N2 - We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus Tn(n≥2), by a noncommutative Tn-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a Z2-symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case.

AB - We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus Tn(n≥2), by a noncommutative Tn-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a Z2-symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case.

KW - Higher abelian gauge theory

KW - Noncommutative torus

KW - S-duality

KW - Strict deformation quantization

KW - String theory

UR - http://www.scopus.com/inward/record.url?scp=84924965393&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924965393&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2015.02.019

DO - 10.1016/j.geomphys.2015.02.019

M3 - Article

VL - 92

SP - 240

EP - 251

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -