Abstract
Recently the calculation of holographic free energy for mass-deformed ABJM model (mABJM) with N=2 supersymmetry and SU(3)×U(1) global symmetry was tackled by Bobev et al. [1]. We solve the associated BPS equations, requiring IR regularity, using a perturbative method proposed by one of us in [2]. In particular, we provide an analytic proof of a crucial conjecture made in [1] based on numerical solutions: that the R-charge values of three chiral multiplets in mABJM should be independent of the IR values of a hypermultiplet scalar, which is holographically dual to the superpotential mass term.
Highlights
Introduction and summarySupersymmetric localization techniques enable us to compute some BPS quantities exactly for supersymmetric gauge field theories in appropriately chosen backgrounds
We provide an analytic proof of a crucial conjecture made in [1] based on numerical solutions: that the R-charge values of three chiral multiplets in mass-deformed ABJM model (mABJM) should be independent of the IR values of a hypermultiplet scalar, which is holographically dual to the superpotential mass term
On gauge field theory side one can compute quantities such as the partition function and Wilson loops when the field theory is put on the sphere
Summary
Supersymmetric localization techniques enable us to compute some BPS quantities exactly for supersymmetric gauge field theories in appropriately chosen backgrounds. For the gravity side analysis, we sometimes deal with, instead of 10/11 dimensional supergravity, their consistently truncated version down to four dimensions Such theories typically contain a number of scalar fields with a potential function whose critical points provide AdS vacua. In this paper we are interested in a non-trivial supersymmetric critical point of N = 8, D = 4, S O (8) gauged supergravity with SU (3) × U (1) unbroken symmetry [18] This solution is 1/4-BPS, so the dual theory should be an N = 2 field theory. The authors of [1] reported an explicit solution where the scalar fields take certain IR values, which are different from the mABJM vacuum at conformality We choose this flow solution as a zeroth order solution for our perturbative approach.
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