Holographic RG flows and symplectic deformations of N=4 gauged supergravity

TL;DR

This paper explores how symplectic deformations affect the structure and solutions of four-dimensional N=4 gauged supergravity with SO(4)×SO(4) gauge group, revealing new RG flows and critical points influenced by these deformations.

Contribution

It introduces the role of symplectic deformation parameters in N=4 gauged supergravity and analyzes their impact on supersymmetric vacua and RG flow solutions.

Findings

Deformation parameters lead to different gauged supergravities with distinct RG flows.

Certain supersymmetric AdS4 critical points only exist for specific deformation values.

Scalar masses and cosmological constants remain unaffected by the deformation phases.

Abstract

We study four-dimensional $N=4$ gauged supergravity with $SO(4)\times SO(4)\sim SO(3)\times SO(3)\times SO(3)\times SO(3)$ gauge group in the presence of symplectic deformations. There are in general four electric-magnetic phases corresponding to each $SO(3)$ factor, but two phases of the $SO(3)$ factors embedded in the $SO(6)$ R-symmetry are fixed. One phase can be set to zero by $SL(2,\mathbb{R})$ transformations. The second one gives equivalent theories for any non-vanishing values and can be set to $\frac{\pi}{2}$ resulting in gauged supergravities that admit $N=4$ supersymmetric $AdS_4$ vacua. The remaining two phases are truely deformation parameters leading to different $SO(4)\times SO(4)$ gauged supergravities. As in the $\omega$-deformed $SO(8)$ maximal gauged supergravity, the cosmological constant and scalar masses of the $AdS_4$ vacuum at the origin of the scalar manifold with $SO(4)\times SO(4)$ symmetry do not depend on the electric-magnetic phases. We find $N=1$ holographic RG flow solutions between $N=4$ critical points with $SO(4)\times SO(4)$ and $SO(3)_{\textrm{diag}}\times SO(3)\times SO(3)$ or $SO(3)\times SO(3)_{\textrm{diag}}\times SO(3)$ symmetries. We also give $N=2$ and $N=1$ RG flows from these critical points to various non-conformal phases. However, contrary to the $\omega$-deformed $SO(8)$ gauged supergravity, there exist non-trivial supersymmetric $AdS_4$ critical points only for particular values of the deformation parameters within the scalar sectors under consideration.