TY - JOUR

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

AU - Mathai, Varghese

AU - Sati, Hisham

N1 - Funding Information:
The authors are grateful to Keith Hannabuss for careful reading of the manuscript and for useful feedback and to David Berman for valuable and crucial comments on the first version. The author are also grateful to the two anonymous referees for very useful suggestions, both on the mathematical and the physical sides, that greatly improved the paper from its original form. V.M. thanks the Australian Research Council for support via ARC Discovery Project grants DP110100072 and DP130103924 . H.S. thanks the National Science Foundation for support via NSF Grant PHY-1102218 .
Publisher Copyright:
© 2015 Elsevier B.V.

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

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U2 - 10.1016/j.geomphys.2015.02.019

DO - 10.1016/j.geomphys.2015.02.019

M3 - Article

AN - SCOPUS:84924965393

SN - 0393-0440

VL - 92

SP - 240

EP - 251

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -