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Journal of High Energy Physics

, 2017:183 | Cite as

Charged structure constants from modularity

  • Diptarka Das
  • Shouvik Datta
  • Sridip Pal
Open Access
Regular Article - Theoretical Physics

Abstract

We derive a universal formula for the average heavy-heavy-light structure constants for 2d CFTs with non-vanishing \( \mathfrak{u}(1) \) charge. The derivation utilizes the modular properties of one-point functions on the torus. Refinements in \( \mathcal{N}=2 \) SCFTs, show that the resulting Cardy-like formula for the structure constants has precisely the same shifts in the central charge as that of the thermodynamic entropy found earlier. This analysis generalizes the recent results by Kraus and Maloney for CFTs with an additional global \( \mathfrak{u}(1) \) symmetry [1]. Our results at large central charge are also shown to match with computations from the holographic dual, which suggest that the averaged CFT three-point coefficient also serves as a useful probe of detecting black hole hair.

Keywords

Conformal Field Theory AdS-CFT Correspondence Black Holes 

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) 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of California San DiegoLa JollaU.S.A.
  2. 2.Institut für Theoretische PhysikEidgenössische Technische Hochschule ZürichZürichSwitzerland

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