The effective potential of gluodynamics in the background of Polyakov loop and colormagnetic field, Michael Bordag (Leipzig U)

Thursday 5 May 2022, 14:15 → 15:45 Europe/Berlin

In SU(N) gluodynamics, the effective potential has minima at non-zero A0-background fields (Polyakov loop) in the two-loop approximation. Also, it has a minimum at non-zero chromomagnetic background field, known as 'Savvidy'-vacuum, or non-Abelian generalization of the Heisenberg-Euler Lagrangian.

We investigate the effective potential when both background fields, A0 and B, are present. The aim is to find a common minimum , in the (A0-B)-plane. We find an unnatural behavior, with large negative values of the effective potential. These are located in the region where the imaginary part sets in. This imaginary part results from the known instability of the chromomagnetic background. However, there are investigations, beginning with the early 80ies of the last century, suggesting that these disappear after the resummation of some classes of diagrams (ring diagrams), keeping the real part of the effective potential unchanged. We come to the conclusion that these results need reconsideration and improvement.