The Cardy Formula from Goldstone Bosons

Abstract

Two dimensional conformal field theories, can be described by their pseudo Goldstone bosons when the conformal symmetry is spontaneously and anomalously broken. We show that the Schwarzian action of these bosons leads to the Cardy formula without using modular invariance. As a result, the Cardy formula applies to conformal field theories on a cylinder and chiral theories in one dimension. This also explains why the Cardy--Verlinde formula for theories on $S^1\times S^{d-2}$ can be written in the form of the Cardy formula of an effective two dimensional theory.

arXiv comment14 pages

References in corpus (14)

• Comments on the Sachdev-Ye-Kitaev model
• Black Hole Entropy from Near-Horizon Microstates
• The Kerr/CFT Correspondence
• Anti De Sitter Space And Holography
• Entropy from Conformal Field Theory at Killing Horizons
• On the Holographic Principle in a Radiation Dominated Universe
• Asymptotic symmetries of AdS_2 and conformal group in d=1
• What is a chiral 2d CFT? And what does it have to do with extremal black holes?
• Models of AdS_2 Backreaction and Holography
• Cargese Lectures on the Kerr/CFT Correspondence
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• Black Holes as Conformal Field Theories on Horizons
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes

Cited by in corpus (1)

• Are Near $Ad{S}_2$ Spacetimes Dual to $Ad{S}_2$ Black Holes?