Partition functions for equivariantly twisted $\mathcal{N}=2$ gauge theories on toric Kähler manifolds

Abstract

We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric Kähler manifolds, with particular emphasis on ${\mathbb{CP}}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct equivariantly twisted theories. Then, using localization, we compute their supersymmetric partition functions. As expected, these receive contributions from a classical, a one-loop, and an instanton term. It turns out that the one-loop term is trivial and that the instanton contributions are localized at the fixed points of the $U(1)$. In fact the full partition function can be re-written in a factorized form with contributions from each of the fixed points. The full significance of this is yet to be understood.

arXiv comment22 pages plus appendices

References in corpus (18)

• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• The Geometry of Supersymmetric Partition Functions
• Supersymmetric Gauge Theories on the Five-Sphere
• Sphere Partition Functions and the Zamolodchikov Metric
• Localization on Hopf surfaces
• On Euclidean spinors and Wick rotations
• Seiberg-Witten Theory and Random Partitions
• Instantons on the 5-sphere and M5-branes
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Seiberg-Witten prepotential from instanton counting
• On certain aspects of string theory/gauge theory correspondence
• Factorization of 5D super Yang-Mills on $Y^{p,q}$ spaces
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• On twisted N=2 5D super Yang-Mills theory
• $\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity
• On N=2 supersymmetric gauge theories on S^2XS^2
• Integration over the u-plane in Donaldson theory

Cited by in corpus (7)

• Rigid 4D N=2 supersymmetric backgrounds and actions
• N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$
• Transversally Elliptic Complex and Cohomological Field Theory
• SYM on Quotients of Spheres and Complex Projective Spaces
• Gauge theories on compact toric manifolds
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• On rigid supersymmetry and notions of holomorphy in five dimensions