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

  • Seyed Morteza HosseiniEmail author
  • Alberto Zaffaroni
Open Access
Regular Article - Theoretical Physics
  • 33 Downloads

Abstract

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 cr into the off-shell functional to be extremized in gravity. We also observe that the similar construction for M2-branes on ℂ4 is equivalent to the ℐ-extremization principle that leads to the microscopic counting for the entropy of magnetically charged black holes in AdS4 × S7. Also this equivalence holds off-shell.

Keywords

AdS-CFT Correspondence Black Holes in String Theory Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Kavli IPMU (WPI), UTIAS, The University of TokyoKashiwaJapan
  2. 2.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  3. 3.INFN, sezione di Milano-BicoccaMilanoItaly

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