The chiral ring of AdS3/CFT2 and the attractor mechanism

Abstract

We study the moduli dependence of the chiral ring in N = (4,4) superconformal field theories, with special emphasis on those CFTs that are dual to type IIB string theory on AdS3xS3xX4. The chiral primary operators are sections of vector bundles, whose connection describes the operator mixing under motion on the moduli space. This connection can be exactly computed using the constraints from N = (4,4) supersymmetry. Its curvature can be determined using the tt* equations, for which we give a derivation in the physical theory which does not rely on the topological twisting. We show that for N = (4,4) theories the chiral ring is covariantly constant over the moduli space, a fact which can be seen as a non-renormalization theorem for the three-point functions of chiral primaries in AdS3/CFT2. From the spacetime point of view our analysis has the following applications. First, in the case of a D1/D5 black string, we can see the matching of the attractor flow in supergravity to RG-flow in the boundary field theory perturbed by irrelevant operators, to first order away from the fixed point. Second, under spectral flow the chiral primaries become the Ramond ground states of the CFT. These ground states represent the microstates of a small black hole in five dimensions consisting of a D1/D5 bound state. The connection that we compute can be considered as an example of Berry's phase for the internal microstates of a supersymmetric black hole.

72 pages (60 + appendices)

References in corpus (6)

• Fuzzballs with internal excitations
• Matching of correlators in AdS_3/CFT_2
• Exact N=4 correlators of AdS(3)/CFT(2)
• Moduli flow and non-supersymmetric AdS attractors
• The Geometric Phase in Supersymmetric Quantum Mechanics
• The Geometric Phase and Gravitational Precession of D-Branes

Cited by in corpus (22)

• A non-renormalization theorem for chiral primary 3-point functions
• String correlators on ${\text{AdS}}_3$: Three-point functions
• Holographic RG flow dual to attractor flow in extremal black holes
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Worldsheet four-point functions in AdS(3)/CFT(2)
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• The Stranger Things of Symmetric Product Orbifold CFTs
• Swampland geometry and the gauge couplings
• Black Hole Berry Phase
• Geometry of Conformal Manifolds and the Inversion Formula
• Scaling Black Holes and Modularity
• Attractive holographic $c$-functions
• Supersymmetric black holes and $T\bar{T}$ deformation
• On the Kähler-Hodge structure of superconformal manifolds
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• The $Ad{S}_3\times S^1$ Chiral Ring
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• Non-Abelian Berry Phase, Instantons and N=(0,4) Supersymmetry
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• The Resolved Elliptic Genus and the D1-D5 CFT
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality