Reduction of Coupling Parameters in Quantum Field Theories

TL;DR

This paper reviews the method of reducing multiple coupling parameters in quantum field theories, illustrating how theories with many couplings can be simplified to theories with a single coupling, including examples with supersymmetry and gauge theories.

Contribution

It introduces a general reduction method for coupling parameters in quantum field theories and provides specific examples involving supersymmetric and gauge theories.

Findings

Reduced theories can have different mathematical structures, including power series, non-integer powers, and logarithmic factors.

An example with supersymmetry shows two solutions, one with N=2 supersymmetry and one without.

In a dual magnetic supersymmetric gauge theory, the reduced Yukawa coupling is uniquely determined by the square of the magnetic gauge coupling.

Abstract

A concise survey is given of the general method of reduction in the number of coupling parameters. Theories with several independent couplings are related to a set of theories with a single coupling. The reduced theories may or may not have particular symmetries. A few have asymptotic power series expansions, others contain non-integer powers and/or logarithmic factors. An example is given with two power series solutions, one with N = 2 Supersymmetry, and one with no known symmetry. In a second example, the reduced Yukawa coupling of the superpotential in a dual magnetic supersymmetric gauge theory is uniquely given by the square of the magnetic gauge coupling with a known factor.