A “Gaussian” approach to computing supersymmetric effective actions

Abstract

For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the action. A method is developed for computing this functional trace by exploiting its similarity to a Gaussian integral. The procedure is extended to superspace, where it is used to compute the low energy effective action obtained by integrating out massive scalar supermultiplets in the presence of a supersymmetric Yang-Mills background.

Nonholomorphic terms inN=2supersymmetric Wilsonian actions and the renormalization group equation

“…In terms of these new variables it is possible to write the Higgs action as 48) and the Yukawa action as…”

“…McArthur and Gargett a "Gaussian approach" to supersymmetric effective actions has been investigated [48].…”

The background field method for $ \mathcal{N} = {2} $ , d3 super Chern-Simons-matter theories

“…Our next goal is to discuss the computations of the superfield coefficients c 1 , c 2 and c 3 . We adopt and generalize for N = 2, d3 case, the procedure developed in [36], [37] and modified for non-Abelian backgrounds in [16]. In some respects, this procedure is similar to that was used in [20] for constructing a gauge invariant derivative expansion of the effective action in the Yang-Mills theory.…”

Nonlinear self-duality and supersymmetry

“…It is worth noting that the BI Lagrangian can be given in the form [14,16] 32) where the complex field χ is a functions of ω andω which satisfies the nonlinear constraint…”

“…In fact, the low-energy effective actions usually have the more general form (see, for instance, [32,33,34]):…”