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Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence

A. Parvizi, M. M. Sheikh-Jabbari, V. Taghiloo

TL;DR

This work extends holography beyond Dirichlet boundaries by embedding gravity in a finite AdS region bounded by a generic timelike surface and enforcing arbitrary boundary conditions via CPSF. It develops a unified deformation framework in which moving the boundary (radial evolution) corresponds to deformations of the boundary QFT, generalizing the Tar{T}-like flow to higher dimensions through operators such as 𝒪_{𝒯̄𝒯} and related terms, and showing equivalence between radial flow and BC deformations. It presents explicit constructions for Dirichlet, Neumann, Conformal, and Conformal Conjugate boundaries, including interpolations between radii and between BCs, and provides detailed GR+n matter examples (Einstein–Scalar, Einstein–Maxwell, Einstein–Chern–Simons, Lovelock) demonstrating how the deformation action 𝒮_{deform} arises from the Brown–York EMT and extrinsic curvature data. Additionally, the paper introduces two classes of hydrodynamic deformations and shows, at least in d=2, a hydrodynamic interpretation of radial evolution, highlighting the broader physical significance of boundary dynamics in holography and setting a program for future exploration of null boundaries, broader asymptotics, and finite-distance dualities.

Abstract

We continue developing the freelance holography program, formulating gauge/gravity correspondence where the gravity side is formulated on a space bounded by a generic timelike codimension-one surface inside AdS and arbitrary boundary conditions are imposed on the gravity fields on the surface. Our analysis is performed within the Covariant Phase Space Formalism (CPSF). We discuss how a given boundary condition on the bulk fields on a generic boundary evolves as we move the boundary to another boundary inside AdS and work out how this evolution is encoded in deformations of the holographic boundary theory. Our analyses here extend the extensively studied T$\bar{\text{T}}$-deformation by relaxing the boundary conditions at asymptotic AdS or at the cutoff surface to be any arbitrary one (besides Dirichlet). We discuss some of the implications of our general freelance holography setting.

Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence

TL;DR

This work extends holography beyond Dirichlet boundaries by embedding gravity in a finite AdS region bounded by a generic timelike surface and enforcing arbitrary boundary conditions via CPSF. It develops a unified deformation framework in which moving the boundary (radial evolution) corresponds to deformations of the boundary QFT, generalizing the Tar{T}-like flow to higher dimensions through operators such as 𝒪_{𝒯̄𝒯} and related terms, and showing equivalence between radial flow and BC deformations. It presents explicit constructions for Dirichlet, Neumann, Conformal, and Conformal Conjugate boundaries, including interpolations between radii and between BCs, and provides detailed GR+n matter examples (Einstein–Scalar, Einstein–Maxwell, Einstein–Chern–Simons, Lovelock) demonstrating how the deformation action 𝒮_{deform} arises from the Brown–York EMT and extrinsic curvature data. Additionally, the paper introduces two classes of hydrodynamic deformations and shows, at least in d=2, a hydrodynamic interpretation of radial evolution, highlighting the broader physical significance of boundary dynamics in holography and setting a program for future exploration of null boundaries, broader asymptotics, and finite-distance dualities.

Abstract

We continue developing the freelance holography program, formulating gauge/gravity correspondence where the gravity side is formulated on a space bounded by a generic timelike codimension-one surface inside AdS and arbitrary boundary conditions are imposed on the gravity fields on the surface. Our analysis is performed within the Covariant Phase Space Formalism (CPSF). We discuss how a given boundary condition on the bulk fields on a generic boundary evolves as we move the boundary to another boundary inside AdS and work out how this evolution is encoded in deformations of the holographic boundary theory. Our analyses here extend the extensively studied T-deformation by relaxing the boundary conditions at asymptotic AdS or at the cutoff surface to be any arbitrary one (besides Dirichlet). We discuss some of the implications of our general freelance holography setting.

Paper Structure

This paper contains 57 sections, 167 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Outline of the Paper.
  3. Review and the setup
  4. Geometric setup
  5. Brief review of covariant phase space formalism
  6. Brief review of gauge/gravity correspondence
  7. Gauge/Gravity correspondence.
  8. Brief review of Freelance Holography I
  9. CPS freedoms in gauge/gravity correspondence.
  10. Holography at finite distance with Dirichlet boundary condition
  11. Bulk theory bounded to region inside
  12. Holography at finite cutoff with Dirichlet boundary conditions, bulk theory
  13. Boundary theory at as a deformation of the boundary theory at
  14. Geometric derivation.
  15. AdS/QFT duality.
  16. ...and 42 more sections

Figures (2)

  • Figure 1: Portion of an asymptotically AdS spacetime bounded by $r\leq r_c$ with a generic timelike boundary $\Sigma_c$. We formulate physics in the shaded region ${\cal M}_c$.
  • Figure 2: Two infinitesimally close boundaries $\Sigma_{r}$ and $\Sigma_{r+\operatorname{d}\!{}r}$ in asymptotically AdS spacetimes.