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Universal features of four-dimensional superconformal field theory on conic space

Open Access
Regular Article - Theoretical Physics

Abstract

Following the set up in arXiv:1408.3393, we study 4d \( \mathcal{N}=1 \) superconformal field theories on conic spaces. We show that the universal part of supersymmetric Rényi entropy S q across a spherical entangling surface in the limit q → 0 is proportional to a linear combination of central charges, 3c − 2a. This is equivalent to a similar statement about the free energy of SCFTs on conic space or hyperbolic space \( {\mathbb{S}}_q^1\times {\mathrm{\mathbb{H}}}^3 \) in the corresponding limit. We first derive the asymptotic formula by the free field computation in the presence of a U (1) R-symmetry background and then provide an independent derivation by studying \( \mathcal{N}=1 \) theories on \( {\mathbb{S}}_{\beta}^1\times {\mathbb{S}}_b^3 \) with a particular scaling \( \beta \sim \frac{1}{\sqrt{q}},b=\sqrt{q} \), which thus confirms the validity of the formula for general interacting \( \mathcal{N}=1 \) SCFTs. Finally we revisit the supersymmetric Rényi entropy of generel \( \mathcal{N}=2 \) SCFTs and find a simple formula for it in terms of central charges a and c.

Keywords

Supersymmetric gauge theory AdS-CFT Correspondence 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.School of Physics and AstronomyTel-Aviv UniversityRamat-AvivIsrael

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