membrane paradigm arises naturally when the boundary fluid lives on a background Galilean manifold.'
author:
- |
    Daniel Brattan$^a$[^1], Joan Camps$^a$[^2], R. Loganayagam$^b$[^3], Mukund Rangamani$^a$[^4]\
    \
    ,\
    \
    ,\
title: |
    [**CFT dual of the AdS Dirichlet problem:\
    Fluid/Gravity on cut-off surfaces**]{}
---

(0,0)(0,0) (380, 330)[DCPT-11/25]{}

Introduction {#s:intro}
============

The AdS/CFT correspondence [@Maldacena:1997re] which postulates a remarkable duality between large $N$ quantum field theories and gravitational dynamics, provides a useful theoretical laboratory to address questions underlying the dynamics of these systems. Not only has it proven useful to obtain quantitative information about the dynamics of strongly coupled field theories, but it also provides a unique perspective into the geometrization of field theoretic concepts.

Since the early days of the AdS/CFT correspondence it has been known that the radial direction of the bulk spacetime encodes in some sense the energy scale of the dual field theory [@Susskind:1998dq]. While the nature of this map is not terribly precise outside of the simple example of pure geometry (dual to the vacuum state of the field theory), it nevertheless provides valuable intuition about certain basic aspects of effective field theory dynamics [@Banks:1998dd; @Peet:1998wn], and has led to the idea of the holographic renormalisation group 