One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

✍ Scribed by Ivan G. Avramidi

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 284 KB
• Volume: 47
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/(sici)1521-3978(199904)47:4<433::aid-prop433>3.0.co;2-g

✦ Synopsis

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many magnetic fieldsº in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of magnetic fieldsº do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of magnetic fieldsº. For two magnetic fieldsº with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d 4Y 5Y 6Y 7 mod 8, the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d 9Y 10Y 11 mod 8 the perturbative vacuum is absolutely stable. In dimensions d 8 mod 8 the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing magnetic fieldsº. The critical value of the coupling constant and the amplitudes of the vacuum magnetic fieldsº are evaluated exactly.