Zoo of flows in a 3d gauged supergravity with periodic potential

TL;DR

This paper constructs and analyzes various solutions in 3D gauged supergravity with a periodic potential, exploring their holographic duals, including deformations of 2D CFTs and black string geometries, with insights into RG flows and $Tar{T}$ deformations.

Contribution

It introduces new AdS/dS solutions with periodic scalar potentials in 3D supergravity, including black strings and analytical near-horizon descriptions, and studies their holographic RG flows and $Tar{T}$ operator behavior.

Findings

Solutions with AdS/dS asymptotics constructed

Black string solutions interpreted as irrelevant operator deformations

Explicit computation of stress-energy tensor and $Tar{T}$ factorization

Abstract

In this paper we construct solutions with AdS/dS asymptotics for $D=3$ truncated gauged supergravity with a periodic scalar potential. In a holographic perspective, assuming Dirichlet boundary conditions, the solutions can be interpreted as deformations of 2d dual CFTs triggered by non-zero vacuum expectation values of irrelevant operators. In addition to the domain wall type solutions, we incorporated in the analysis a black string solution, which can also be interpreted as a deformation by VEV of an irrelevant operator. Generalizing the flows to finite temperature, we find that the corresponding geometries are singular but have horizons. For certain flows, we provide an analytical description near the horizon region. For an exact RG flow solution, we explicitly compute the Brown-York stress-energy tensor on a cutoff surface and show that the $T\overline{T}$ operator factorizes along the holographic RG flow. We also define an effective, scale-dependent deformation parameter $\mu(\phi)$, whose running is governed by the scalar field at the cutoff.