A perturbative study of holographic mABJM theory

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.

Towards an explicit construction of de Sitter solutions in classical supergravity

“…Just like our previous works [12][13][14][15], the result here lends further support to the perturbative prescription as a powerful alternative to numerical analyses of supergravity equations which are generically nonlinear. We comment that an important requirement for our prescription is an explicit, and preferably simple, unperturbed solution, like (3.2).…”

“…Let us comment that this approach is reminiscent of recent works [12][13][14][15], where supergravity solutions in various holographic contexts are constructed using a perturbative prescription. A notable difference here is that we are looking for non-supersymmetric solutions, so instead of first-order BPS relations we have second-order differential equations, and the analysis is more challenging.…”

The Hamilton-Jacobi equation and holographic renormalization group flows on sphere

“…More recently, the present authors proposed and pursued a perturbative prescription which allows one to obtain the holographic action as a power series in UV expansion parameters. The conjectures based on numerical results are partly confirmed for N = 2 * and N = 1 * deformations of N = 4 super Yang-Mills [58,59], and for mABJM theory [60] which is obtained as a nontrivial fixed point of renormalization group after one of bifundamental chiral multiplet is given superpotential mass and integrated out. For the mass deformation of Brandhuber-Oz theory [25,[61][62][63], where numerical results did not lead to a definitive conjecture on analytic relations, we managed to obtain the holographic free energy in closed form, from the resummation of the perturbative results.…”

The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows on Sphere

“…More recently, the present authors proposed and pursued a perturbative prescription which allows one to obtain the holographic action as a power series in UV expansion parameters. The conjectures based on numerical results are partly confirmed for N = 2 * and N = 1 * deformations of N = 4 super Yang-Mills [57,58], and for mABJM theory [59] which is obtained as a nontrivial fixed point of renormalization group after one of bifundamental chiral multiplet is given superpotential mass and integrated out. For the mass deformation of Brandhuber-Oz theory [25,[60][61][62], where numerical results did not lead to a definitive conjecture on analytic relations, we managed to obtain the holographic free energy in closed form, from the resummation of the perturbative results.…”