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 CP2 for 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. © 2016, The Author(s).

Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants / Bershtein, M; Bonelli, Giulio; Ronzani, Massimiliano; Tanzini, Alessandro. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2016:7(2016), pp. 1-39. [10.1007/JHEP07(2016)023]

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

Bonelli, Giulio;Ronzani, Massimiliano;Tanzini, Alessandro
2016-01-01

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 CP2 for 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. © 2016, The Author(s).
2016
2016
7
1
39
23
https://doi.org/10.1007/JHEP07(2016)023
https://arxiv.org/abs/1509.00267
Bershtein, M; Bonelli, Giulio; Ronzani, Massimiliano; Tanzini, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15961
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