Warm \(p\)-soup and near extremal black holes. (English) Zbl 1291.81336

Summary: We consider a model of \(D\)-dimensional supergravity coupled to elementary \(p\)-branes. We use gravitational arguments to deduce the low energy effective theory of \(N\) nearly parallel branes. This is a \((p+1)\)-dimensional scalar field theory, where the scalars represent the positions of the branes in their transverse space. We propose that the same theory in a certain temperature regime describes a ‘soup’ of strongly interacting branes, giving a microscopic description of near extremal black \(p\)-branes. We use natural approximations to estimate the energy density of this soup as a function of the physical parameters; \(N\), temperature, brane tension and gravitational coupling. We also characterize the horizon radius, measured in the metric natural to the branes, with the thermal vev of the scalars. For both quantities we find agreement with the corresponding supergravity black brane results. Surprisingly, beyond the physical parameters, we are naturally able to reproduce certain irrational factors such as \(\pi\)s. We comment on how these ideas may explain why black hole thermodynamics arises in gauge theories with holographic duals at finite temperature.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
80A10 Classical and relativistic thermodynamics
83C57 Black holes
83E50 Supergravity
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
Full Text: DOI arXiv