Proving the equivalence of c-extremization and its gravitational dual for all toric quivers

• Published in: The journal of high energy physics Vol. 2019; no. 3; pp. 1 - 34
• Main Authors: Hosseini, Seyed Morteza, Zaffaroni, Alberto
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black holes; Black Holes in String Theory; Branes; Classical and Quantum Gravitation; Elementary Particles; Equivalence; Gravitation theory; High energy physics; Optimization; Parameterization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Black Holes in String Theory; AdS-CFT Correspondence; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP03(2019)108

A bstract The gravitational dual of c -extremization for a class of (0 , 2) two-dimensional theories obtained by twisted compactifications of D3-brane gauge theories living at a toric Calabi-Yau three-fold has been recently proposed. The equivalence of this construction with c -extremization has been checked in various examples and holds also off-shell. In this note we prove that such equivalence holds for an arbitrary toric Calabi-Yau. We do it by generalizing the proof of the equivalence between a -maximization and volume minimization for four-dimensional toric quivers. By an explicit parameterization of the R-charges we map the trial right-moving central charge c r into the off-shell functional to be extremized in gravity. We also observe that the similar construction for M2-branes on ℂ 4 is equivalent to the ℐ-extremization principle that leads to the microscopic counting for the entropy of magnetically charged black holes in AdS 4 × S 7 . Also this equivalence holds off-shell.