Holography for stress-energy tensor flows

TL;DR

This work advances holographic duals for general stress-energy tensor deformations by linking mixed boundary conditions to metric-flow equations, extending beyond the well-studied T T̄ case to arbitrary dimensions. Using the metric-flow framework, the authors show how Planar AdS black holes encode the deformed boundary data and demonstrate that the resulting energy flow ∂_τ E = V O(t_α) matches large-N field-theory expectations. They derive a general commuting condition C(O_1,O_2)=0 for deformations and construct infinite families of mutually commuting deformations, enabling rich holographic models with flexible boundary conditions. The results broaden the holographic toolkit for TT̄-like deformations and point to new directions for nonperturbative bulk physics, conformal anomalies, and finite-N extensions in AdS/CFT.

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.