Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants

TL;DR

This paper explores the structure of supergraphs in 4d supersymmetric gauge theories and their lower-dimensional reductions, revealing connections between nonrenormalization theorems and effective Lagrangians across dimensions.

Contribution

It establishes a link between 4d nonrenormalization theorems and their low-dimensional analogs through multiloop supergraph analysis.

Findings

Multiloop supergraphs determine effective charge renormalization in 4d.

Low-energy effective Lagrangians encode the metric on moduli space.

Nonrenormalization theorems are related across dimensions.

Abstract

We analyze the structure of multiloop supergraphs contributing to the effective Lagrangians in 4d supersymmetric gauge theories and in the models obtained from them by dimensional reduction. When d=4, this gives the renormalization of the effective charge. For d < 4, the low-energy effective Lagrangian describes the metric on the moduli space of classical vacua. These two problems turn out to be closely related. In particular, we establish the relationship between the 4d nonrenormalization theorems (in minimal and extended supersymmetric theories) and their low--dimensional counterparts.