A High Temperature Phase Transition in Weakly Coupled Large N Gauge Theories on a Three-sphere
We argue that weakly coupled 3+1 dimensional large N SU(N) gauge theories, with 't Hooft coupling {gamma}, compactified on a three-sphere of radius R, exhibit a novel second order phase transition at a temperature T{sub c} = C{radical}{gamma} R. The known constant C depends on the details of the gauge theory. The phase transition is characterized by a change in the eigenvalue distributions of the fields. Above the transition, the only eigenvalues which condense are those of the lowest Kaluza-Klein mode of the spatial gauge field Ai on the three-sphere. Below the transition the eigenvalues of the lowest Kaluza-Klein mode of an additional field condense. We discuss in particular the examples of pure Yang-Mills theory and of the N = 4 supersymmetric Yang-Mills theory.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 908992
- Report Number(s):
- SLAC-PUB-12570; arXiv:0706.2861; TRN: US0703809
- Country of Publication:
- United States
- Language:
- English
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