Zooming in on AdS$_3$/CFT$_2$ near a BPS Bound

TL;DR

The paper introduces a near-BPS decoupling limit of AdS$_3$/CFT$_2$ obtained by an Inönü–Wigner contraction of $so(2,2)u(1)u(1)$, producing a relativistic algebra with a dilatation but without conformal generators. In 2D, adding a second $u(1)$ yields two copies of the centrally extended 2D Poincaré algebra $P_2^c$, and the bulk dual is a novel non-Lorentzian pseudo-Newton–Cartan geometry; the contraction maps the AdS$_3$ CS theory to a theory of pseudo-NC gravity with a well-defined phase space when the radial component for the $u(1)$ connection is fixed. The asymptotic symmetry algebra becomes left- and right-moving warped Virasoro algebras, providing a controlled non-AdS holographic setting that preserves scale invariance and offers a tractable arena to study holography, phase-space mappings, and bulk matter couplings in a contracted regime. The work opens avenues for higher-dimensional generalizations, connections to Spin Matrix Theory, and potential string-theory realizations of pseudo-NC holography, with implications for nonrelativistic holography and bulk reconstruction in near-BPS sectors.

Abstract

Any $(d+1)$-dimensional CFT with a $U(1)$ flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of $so(2,d+1)\oplus u(1)$ that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second $u(1)$ we find a contraction of two copies of $sl(2,\mathbb{R})\oplus u(1)$ to two copies of $P_2^c$, the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on $sl(2,\mathbb{R})\oplus u(1)$ and the entire phase space of asymptotically AdS$_3$ spacetimes are well-behaved in the corresponding limit if we fix the radial component for the $u(1)$ connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS$_3$ holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra.