Abstract
We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d \mathcal{N}=4𝒩=4 ADHM theory with a gauge group U(N)U(N), an adjoint hypermultiplet and ll hypermultiplets which can describe a stack of NN M2-branes at A_{l-1}Al−1 singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.
Highlights
The technique of supersymmetric localization allows for exact computations of observables in quantum field theories with a certain minimum amount of supersymmetry as pioneered by Pestun [1].It was shown in [3] that the partition function on a three-sphere S3 of a three-dimensional gauge theory with N ≥ 3 supersymmetry reduces to a matrix model via the localization.For three-dimensional theories with N = 4 supersymmetry the sphere partition functions can be decorated by either of two types of half-BPS local operators; the Coulomb
In this paper we analytically evaluate the sphere correlators of the Coulomb branch operators for the ADHM theory in the Fermi-gas formulation
We evaluated the large N correlation functions of the Coulomb branch operators for 3d N = 4 ADHM theory in the Fermi-gas formulation
Summary
The technique of supersymmetric localization allows for exact computations of observables in quantum field theories with a certain minimum amount of supersymmetry as pioneered by Pestun [1] (see [2] for reviews) It was shown in [3] that the partition function on a three-sphere S3 of a three-dimensional gauge theory with N ≥ 3 supersymmetry reduces to a matrix model via the localization. The protected correlation functions of the Higgs branch operators or the Coulomb branch operators in 3d N = 4 supersymmetric field theories are encoded by one-dimensional topological quantum mechanical models [13, 14]. In this paper we analytically evaluate the sphere correlators of the Coulomb branch operators for the ADHM theory in the Fermi-gas formulation.
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