TOPOLOGICAL OBJECTS AND CONFINEMENT ON THE LATTICE

TL;DR

This paper explores topological objects relevant to confinement in lattice gauge theories and derives an effective quantum string theory in four dimensions, addressing anomalies and corrections to the Nambu-Goto action.

Contribution

It introduces a detailed analysis of topological objects like monopoles and hybrids in confinement and derives a consistent quantum string theory in four dimensions from field theory.

Findings

Topological objects may be crucial for confinement mechanisms.

The Jacobian correction leads to a conformally invariant string action in D=4.

Quantum string theory in four dimensions is achievable with anomaly cancellation.

Abstract

First we discuss various topological objects (monopoles, ``minopoles'' and ``hybrids'') which may be important for the confinement mechanism in various abelian projections. The second topic is the string between quark and antiquark. The standard quantum string with the Nambu-Goto action exists only in D=26. If we start from the field theory, in which the string excitations exist, and change the variables in the path integral to the string variables, then the Jacobian appears. This Jacobian generates the correction to the Nambu-Goto action. For this effective action the conformal anomaly cancels in D=4. Thus we get the quantum string theory in D=4.