TY - JOUR

T1 - Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

AU - Bershtein, Mikhail

AU - Bonelli, Giulio

AU - Ronzani, Massimiliano

AU - Tanzini, Alessandro

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Abstract: We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗theory on ℙ 2for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

AB - Abstract: We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗theory on ℙ 2for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

KW - Differential and Algebraic Geometry

KW - Extended Supersymmetry

KW - Supersymmetric gauge theory

KW - Topological Field Theories

UR - http://www.scopus.com/inward/record.url?scp=84978086031&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2016)023

DO - 10.1007/JHEP07(2016)023

M3 - Article

AN - SCOPUS:84978086031

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 23

ER -