Free Yang-Mills vs. Toric Sasaki-Einstein

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.

18 pages, 7 figures, latex, comments and a reference added (v2), explanation improved and references added (v3), a reference added (v4)

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• $K^{-}d\to \pi \Sigma n$ reactions and structure of the $\Lambda (1405)$