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

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.

38 pages, v2: references added and typos corrected, v3: references added, journal version

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Cited by in corpus (20)

• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Non-Relativistic Gravity and its Coupling to Matter
• Relating non-relativistic string theories
• Review on Non-Relativistic Gravity
• Limits of JT gravity
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
• Oddity in nonrelativistic, strong gravity
• Black Hole Spectroscopy and AdS${}_2$ Holography
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Galilean free Lie algebras
• Matrix Theory Reloaded: A BPS Road to Holography
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Non-Relativistic Limits of Colored Gravity in Three Dimensions
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Conformal Lie algebras via deformation theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory