On consistent truncations in $ \mathcal{N} $ = 2* holography

Venkat Balasubramanian,Alex Buchel

doi:10.1007/jhep02(2014)030

Venkat Balasubramanian, Alex Buchel

Open Access

https://doi.org/10.1007/jhep02(2014)030

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Abstract

Although Pilch-Warner (PW) gravitational renormalization group flow [arXiv:hep-th/0004063] passes a number of important consistency checks to be identified as a holographic dual to a large-$N$ $SU(N)$ ${\cal N}=2^*$ supersymmetric gauge theory, it fails to reproduce the free energy of the theory on $S^4$, computed with the localization techniques. This disagreement points to the existence of a larger dual gravitational consistent truncation, which in the gauge theory flat-space limit reduces to a PW flow. Such truncation was recently identified by Bobev-Elvang-Freedman-Pufu (BEFP) [arXiv:1311.1508]. Additional bulk scalars of the BEFP gravitation truncation might lead to destabilization of the finite-temperature deformed PW flows, and thus modify the low-temperature thermodynamics and hydrodynamics of ${\cal N} =2^*$ plasma. We compute the quasinormal spectrum of these bulk scalar fields in the thermal PW flows and demonstrate that these modes do not condense, as long as the masses of the ${\cal N}=2^*$ hypermultiplet components are real.

Highlights

IntroductionOne can prove that there does not exist a choice of a scheme in which the free energy of the S4-compactified PW flow would agree with the free energy of the N = 2∗ theory computed in the large-N , and large λ, saddle point of the corresponding matrix integral [6]
The question “What makes the PW vacuum (1.3) special?” was answered in [4]: turns out, supersymmetric formulation of N = 2∗ gauge theory on S4, in the planar limit and at large ’t Hooft coupling, lifts all the Coulomb branch moduli, except for a single point; this single point, in the S4 decompactification limit is precisely the vacuum (1.3)
Compare to PW effective action, BEFP action contains a triplet of SU(2)V bulk scalar fields, and one additional neutral scalar

Summary

Introduction

One can prove that there does not exist a choice of a scheme in which the free energy of the S4-compactified PW flow would agree with the free energy of the N = 2∗ theory computed in the large-N , and large λ, saddle point of the corresponding matrix integral [6] It was suggested in [6] ( in [9,10,11]) that this free energy puzzle points to the existence of an “enlarged” holographic truncation of the N = 2∗ gauge theory, which in addition to PW bulk scalars α and χ contains additional scalars representing the coupling of the gauge theory to S4 background metric, necessary to insure the curved-space supersymmetry [5].

Objectives

Conclusion