A geometric dual of c-extremization

TY - JOUR

T1 - A geometric dual of c-extremization

AU - Couzens, Christopher

AU - Gauntlett, Jerome P.

AU - Martelli, Dario

AU - Sparks, James

PY - 2019/1/29

Y1 - 2019/1/29

N2 - We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS4. We also study many specific examples of the type AdS3 × T2 × Y5, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dual to these solutions can arise from the compactification on T2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

AB - We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS4. We also study many specific examples of the type AdS3 × T2 × Y5, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dual to these solutions can arise from the compactification on T2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

KW - AdS-CFT Correspondence

KW - Black Holes in String Theory

KW - Differential and Algebraic Geometry

KW - Supersymmetric Gauge Theory

UR - http://www.scopus.com/inward/record.url?scp=85060908930&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2019)212

DO - 10.1007/JHEP01(2019)212

M3 - Article

AN - SCOPUS:85060908930

SN - 1126-6708

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 1

M1 - 212

ER -