On the confining potential in 4d $SU(N_c)$ gauge theory with dilaton

TL;DR

This paper derives a general formula for the quark-quark interaction potential in 4d SU(N_c) gauge theory with a dilaton, linking it to confinement mechanisms and incorporating string theory elements.

Contribution

It introduces a novel formula for the interquark potential based on superstring-inspired models and explores the role of the dilaton-gluon coupling in confinement.

Findings

Derived a general potential formula including the Dick confining potential.

Linked the potential to dilaton-gluon coupling and vacuum condensates.

Discussed incorporation of the axion field consistent with string theory.

Abstract

Using the formal analogy between the Dick superstring inspired model of ref.[6] and the problem of building of Eguchi Hanson metric in 4d N=2 harmonic superspace (hs), we derive a general formula for the quark-quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton-gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10d type IIB superstring requirements. Others features are also discussed.