't Hooft Loop Average in the Vicinity of the Londons' Limit and the Quartic Cumulant of the Field Strength Tensors

TL;DR

This paper analyzes the next-to-leading correction to the 't Hooft loop average in the Abelian Higgs Model near the Londons' limit, revealing the emergence of the quartic cumulant due to finite coupling effects.

Contribution

It derives the next-to-leading term in the string representation of the 't Hooft loop, highlighting the role of the quartic cumulant beyond the Londons' limit.

Findings

The quartic cumulant appears due to finite coupling effects.

The correction depends on the correlation radius of the Higgs field.

The analysis extends understanding of the 't Hooft loop in the Abelian Higgs Model.

Abstract

The next-to-leading term in the weight factor of the string representation of the 't Hooft loop average defined on the string world-sheet is found in the Abelian Higgs Model near the Londons' limit. This term emerges due to the finiteness of the coupling constant and, in contrast to the Londons' limit, where only the bilocal cumulant in the expansion of the 't Hooft average survived, leads to the appearance of the quartic cumulant. Apart from the Londons' penetration depth of the vacuum, which was a typical fall-off scale of the bilocal cumulant, the quartic cumulant depends also on the other characteristic length of the Abelian Higgs Model, the correlation radius of the Higgs field.