Free Yang-Mills vs. Toric Sasaki-Einstein

TL;DR

This paper investigates the ratio of free to strongly coupled entropy in N=1 SCFTs dual to toric Sasaki-Einstein manifolds, finding it consistently near the known 4/3 factor for N=4 super Yang-Mills.

Contribution

It extends the analysis of entropy ratios to a broad class of N=1 SCFTs and provides explicit geometric data for new toric Sasaki-Einstein manifolds.

Findings

Entropy ratio remains close to 4/3 across many N=1 SCFTs.

Explicit volumes and central charges for new toric Sasaki-Einstein manifolds.

The ratio's narrow range suggests a universal behavior.

Abstract

It has been known that the Bekenstein-Hawking entropy of the black hole in AdS_5 * S^5 agrees with the free N=4 super Yang-Mills entropy up to the famous factor 4/3. This factor can be interpreted as the ratio of the entropy of the free Yang-Mills to the entropy of the strongly coupled Yang-Mills. In this paper we compute this factor for infinitely many N=1 SCFTs which are dual to toric Sasaki-Einstein manifolds. We observed that this ratio always takes values within a narrow range around 4/3. We also present explicit values of volumes and central charges for new classes of toric Sasaki-Einstein manifolds.