A Quantum Perfect Lattice Action for Monopoles and Strings

TL;DR

This paper derives a quantum perfect lattice action for monopoles and strings in four dimensions, ensuring the lattice spectrum matches the continuum, and provides explicit operators for static potential calculations.

Contribution

It analytically constructs a quantum perfect lattice action for monopoles and strings, preserving continuum properties and enabling precise potential evaluations.

Findings

Lattice spectrum matches continuum theory

String interactions become strong with weak monopole interactions

Static potential and string tension are estimated analytically

Abstract

A quantum perfect lattice action in four dimensions can be derived analytically as a renormalized trajectory when we perform a block spin transformation of monopole currents in a simple but non-trivial case of quadratic monopole interactions. The spectrum of the lattice theory is identical to that of the continuum theory. The perfect monopole action is transformed exactly into a lattice action of a string model. A perfect operator evaluating a static potential between electric charges is also derived explicitly. If the monopole interactions are weak as in the case of infrared SU(2) QCD, the string interactions become strong. The static potential and the string tension is estimated analytically by the use of the strong coupling expansion and the continuum rotational invariance is restored completely.