Tachyon condensation in a chromomagnetic background field and the groundstate of QCD

TL;DR

This paper proposes a new approach to stabilize the chromomagnetic vacuum in SU(2) by modeling the tachyonic mode as a condensate undergoing a phase transition, avoiding the instability and imaginary part issues.

Contribution

It introduces a novel solution by treating the tachyonic mode as a condensate within a simplified O(2)-model framework using the CJT formalism, providing a stable ground state in low-temperature QCD.

Findings

A stable minimum of the effective action is found at low temperatures.

The model predicts a phase transition restoring symmetry at a critical temperature.

The approach avoids the imaginary part problem in the effective action.

Abstract

I consider the chromomagnetic vacuum in SU(2). The effective Lagrangian in one loop approximation is known to have a minimum below zero which results in a spontaneously generated magnetic field. However, this minimum is not stable; the effective action has an imaginary part. Over the past decades, there were many attempts to handle this situation which all were at some point unsatisfactory. I propose an idea for a new solution by assuming that the tachyonic mode, at low temperature, acquires a condensate and, as a result, undergoes a phase transition like in the Higgs model. I consider the approximation where all gluon modes are dropped except for the tachyonic one. For this mode, we have a O(2)-model with quartic self-interaction in two dimensions. I apply the CJT (2PI) formalism in the Hartree approximation. As a result, at zero and low temperatures, a minimum of the effective action at a certain value of the condensate and of the background fields is observed and there is no imaginary part. Raising the temperature, this minimum becomes shallower and at a critical temperature, the perturbative state becomes that with lower effective potential; the symmetry is restored. The physical interpretation says that the unstable mode creates tachyons until these come into equilibrium with their repulsive self-interaction and form a condensate. The relation to the Mermin-Wagner theorem is discussed. }