Towards a diagrammatic derivation of the Veneziano–Yankielowicz–Taylor superpotential

R.A. Janik,J. Ambjørn

doi:10.1016/j.physletb.2003.07.018

R.A. Janik, J. Ambjørn

Open Access

https://doi.org/10.1016/j.physletb.2003.07.018

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Abstract

We show how it is possible to integrate out chiral matter fields in N=1 supersymmetric theories and in this way derive in a simple diagrammatic way the NfSlogS−SlogdetX part of the Veneziano–Yankielowicz–Taylor superpotential.

Highlights

The recent renewed interest in the calculation of the glueball superpotential via matrix models [1] has led to an understanding of how to extract the nonlogarithmic part of these superpotentials by ordinary diagrammatic methods [2]
We are still left without a simple diagrammatic derivation of the logarithmic part of the glueball superpotential, the so called VenezianoYankielowicz-Taylor superpotential
This effective Lagrangian was originally derived for a pure N = 1 U(Nc) gauge theory by Veneziano and Yankielowicz [3] by anomaly matching and, by the same method, generalized to a U(Nc) theory with Nf flavors in the fundamental representation by Taylor, Veneziano and Yankielowicz [4]

Summary

Introduction

The recent renewed interest in the calculation of the glueball superpotential via matrix models [1] has led to an understanding of how to extract the nonlogarithmic part of these superpotentials by ordinary diagrammatic methods [2]. We are still left without a simple diagrammatic derivation of the logarithmic part of the glueball superpotential, the so called VenezianoYankielowicz-Taylor superpotential This effective Lagrangian was originally derived for a pure N = 1 U(Nc) gauge theory by Veneziano and Yankielowicz [3] by anomaly matching and, by the same method, generalized to a U(Nc) theory with Nf flavors in the fundamental representation by Taylor, Veneziano and Yankielowicz [4]. Where we took Wtree = 0 and fixed the auxiliary mass M = 1 (it will be clear from the arguments below that the result is independent of M) This is no longer a free field theory, but there are significant simplifications if we only want to extract the tr W2 dependence. Thanks to the above property we may find the full QQ propagator in terms of the α 1-point function which we will denote by F : p2

W α πα

Discussion