Gluing Nekrasov Partition Functions
Abstract
In this paper we summarise the localisation calculation of 5D super YangMills on simply connected toric SasakiEinstein (SE) manifolds. We show how various aspects of the computation, including the equivariant index, the asymptotic behaviour and the factorisation property are governed by the combinatorial data of the toric geometry. We prove that the perturbative partition function on a simply connected SE manifold corresponding to an ngon toric diagram factorises to n copies of perturbative part (zero instanton sector) of the Nekrasov partition function. This leads us to conjecture a prescription for the computation of the complete partition function, by gluing n copies of the full Nekrasov partition functions. This work is a generalisation of some earlier computation carried out on Y ^{ p, q } manifolds, whose moment map cone has a quadrangle base and our result is valid for manifolds whose moment map cones have pentagon base, hexagon base, etc. The algorithm we used for dealing with general cones may also be of independent interest.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 July 2015
 DOI:
 10.1007/s0022001523517
 arXiv:
 arXiv:1403.2945
 Bibcode:
 2015CMaPh.337..785Q
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Symplectic Geometry
 EPrint:
 37 pages, references added, typos corrected