When UV and IR Collide: Inequivalent CFTs From Different Foliations Of AdS

TL;DR

This paper investigates how different foliations of AdS space lead to inequivalent boundary CFTs, showing that the choice of boundary surface affects correlators and the bulk duals, especially near horizons.

Contribution

It demonstrates that CFTs defined on different boundary surfaces of AdS are distinct, impacting the understanding of their bulk duals and horizon physics.

Findings

Correlators differ across global, Rindler, and Poincaré CFTs.

Bulk duals agree near horizons but diverge deeper inside.

Implications for BTZ black hole duals and horizon modifications.

Abstract

In the AdS/CFT correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This difference arises because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincar\'e coordinates for AdS$_3$. We refer to these as global-CFT, Rindler-CFT and Poincar\'e-CFT respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of AdS$_3$, we discuss the implications of our results for bulk duals of periodically-identified Poincar\'e and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semi-classical BTZ geometry close to the horizons.