Holography for stress-energy tensor flows

TL;DR

This paper explores how holography describes stress-energy tensor deformations across dimensions, using metric flow equations to connect boundary conditions with bulk solutions, and verifies the approach with black hole examples.

Contribution

It introduces a metric flow framework for holographic stress-energy deformations and extends boundary conditions to families of commuting deformations.

Findings

Deformed energies follow flow equations consistent with field theory.

Mixed boundary conditions arise naturally from metric flow solutions.

The approach is validated with planar AdS black hole analysis.

Abstract

We study the holographic description for general stress-energy tensor deformations in arbitrary dimensions using the metric flow approach. Mixed boundary conditions corresponding to these deformations emerge from solutions to the metric flow equations. To test this proposal, we analyze planar anti-de Sitter black holes with such boundary conditions and find that the deformed energies satisfy flow equations consistent with the field theory interpretation. We further derive the commuting condition for stress-energy tensor deformations and extend the mixed boundary condition description to accommodate families of commuting deformations.