Vacuum Energies and Effective Potential in Light-Cone Field Theories

TL;DR

This paper calculates vacuum energies and effective potentials in light-cone field theories, demonstrating independence from quantization surface angles and explicitly performing renormalization in several models, including large N limits.

Contribution

It introduces a method to define vacuum energies unambiguously using interpolating quantization surfaces and applies it to various models, including two-dimensional QCD.

Findings

Vacuum energies are independent of the interpolating angle.

Explicit renormalization of the effective potential is achieved.

Vacuum energies in large N models lead to gap equations.

Abstract

Vacuum energies are computed in light-cone field theories to obtain effective potentials which determine vacuum condensate. Quantization surfaces interpolating between the light-like surface and the usual spatial one are useful to define the vacuum energies unambiguously. The Gross-Neveu, SU(N) Thirring, and O(N) vector models are worked out in the large $N$ limit. The vacuum energies are found to be independent of the interpolating angle to define the quantization surface. Renormalization of effective potential is explicitly performed. As an example of the case with nonconstant order parameter, two-dimensional QCD is also studied. Vacuum energies are explicitly obtained in the large $N$ limit which give the gap equation as the stationary point.