Effective Potentials and the Vacuum Structure of Quantum Field Theories
Abstract
I review some older work on the effective potentials of quantum field theories, in particular the use of anomalous symmetries to constrain the form of the effective potential, and the background field method for evaluating it perturbatively. Similar techniques have recently been used to great success in studying the effective superpotentials of supersymmetric gauge theories, and one of my motivations is to present some of the older work on nonsupersymmetric theories to a new audience. The GrossNeveu model exhibits the essential features of the techniques. In particular, we see how rewriting the Lagrangian in terms of an appropriate composite background field and performing a perturbative loop expansion gives nonperturbative information about the vacuum of the theory (the fermion condensate). The effective potential for QED in a constant electromagnetic background field strength is derived, and compared to the analogous calculation in nonAbelian YangMills theory. The YangMills effective potential shows that the ``perturbative'' vacuum of YangMills theory is unstable, and the true vacuum has a nontrivial gauge field background. Finally, I describe how some of the limitations seen in the nonsupersymmetric theories are removed by supersymmetry, which allows for exact computation of the effective superpotential in many cases.
 Publication:

arXiv eprints
 Pub Date:
 July 2004
 arXiv:
 arXiv:hepth/0407084
 Bibcode:
 2004hep.th....7084K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 30 pages, 4 figures