Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
May, 201036 pages
Published in:
- JHEP 08 (2010) 015
e-Print:
- 1005.2181 [hep-th]
Report number:
- TIFR-TH-10-09
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Abstract: (arXiv)
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 \mu-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 \to \infty 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.Note:
- 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHEP
- M(atrix) Theories
- 1/N Expansion
- Brane Dynamics in Gauge Theories
- Confinement
- potential: chemical
- temperature: high
- condensation
- expansion 1/N
- expansion 1/d
- dimensional reduction
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