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arXiv · hep-th/0512101

Half-BPS Geometries and Thermodynamics of Free Fermions

Simone Giombi·Manuela Kulaxizi·Riccardo Ricci·Diego Trancanelli
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Abstract

Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the "bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null singularity and, by general arguments, is expected to develop a finite area horizon once stringy corrections are included. By introducing a stretched horizon, we propose a way to match the entropy of the fermions with the entropy of the geometry in the low temperature regime. In the opposite limit of high temperature, the solution resembles a dilute gas of D3 branes. Also in this case the ADM mass of the geometry agrees with the thermal energy of the fermions.

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Simone Giombi, Manuela Kulaxizi, Riccardo Ricci, Diego Trancanelli. 2007-03-07. Half-BPS Geometries and Thermodynamics of Free Fermions. https://doi.org/10.1088/1126-6708%2F2007%2F01%2F067

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