Twisted supersymmetric 5D Yang-Mills theory and contact geometry

By J. Källén, M. Zabzine. 2012

215 citations recorded by the source corpus.

A bstractWe extend the localization calculation of the 3D Chern-Simons partition func- tion over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N = 1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five- dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on S5 for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90’s, and in a way it is covariantization of their ideas for a contact manifold.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1353f63179d06c5bf0e95f92bf4e12653ebe57b6

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Citations in the corpus

5-dim superconformal index with enhanced En global symmetry (2012, background): “See the recent work [45, 46, 47] for the perturbative part of the partition function of 5-dim supersymmetric YM theory on S(5).”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, methodology): “For further details regarding the contact geometry involved in this case, the reader may consult [5] and the references therein.”
Exact results for five-dimensional superconformal field theories with gravity duals (2012, result): “As shown in [23] (see [21, 22] for earlier work and also [40]), the S5 partition function of 5d Yang-Mills theory with gauge group G and matter hyper multiplets in representations Ri takes the form”
Seiberg-Witten theories on ellipsoids (2012, background): “Also, in [17, 18, 19] another construction of supersymmetric gauge theories in three or five dimensions has been discussed in connection with contact geometry, and moreover some exact results have been worked out for theories on 3D Seifert manifolds.”
M5-branes from gauge theories on the 5-sphere (2012, methodology): “See also [24, 26] which study the same equations.”
Supersymmetric field theories on three-manifolds (2012, background): “1 For related work in two and five dimensions, see [14-16] and [17-20], respectively.”