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Thermodynamics of large N gauge theories with chemical potentials in a 1/D expansion

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Abstract

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1 + D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the μ − T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D → ∞ limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it.

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  1. Department of Theoretical Physics Tata Institute of Fundamental Research Homi Bhabha Rd, Mumbai, 400005, India

    Takeshi Morita

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ArXiv ePrint: 1005.2181

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Morita, T. Thermodynamics of large N gauge theories with chemical potentials in a 1/D expansion. J. High Energ. Phys. 2010, 15 (2010). https://doi.org/10.1007/JHEP08(2010)015

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