2016/06/22 by Matteo Beccaria, Guido Macorini
Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge theory #Hamiltonian (control theory) #Instanton #Modular invariance #Particle physics theoretical and experimental studies #Partition function (quantum field theory) #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #Scalar field #Scalar potential #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1007/jhep07(2016)066
25 pages, one pdf figure. v2: references added
arxiv created 2016/06/22 · openalex created_date 2016/06/24 · openalex publication_date 2016/07/01 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
We study the low energy effective action of the Ω-deformed N=2∗ SU(2) gauge theory. It depends on the deformation parameters ϵ 1, ϵ 2, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane ((m)/(\upepsilon1),(\upepsilon2)/(\upepsilon1)) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ϵ 2 → 0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.