Supersymmetric gauge theories with a free algebra of invariants

TL;DR

This paper investigates the low-energy behavior of N=1 supersymmetric gauge theories with unconstrained gauge invariants, revealing conditions for the existence of a zero superpotential branch and analyzing specific examples like SO(13).

Contribution

It characterizes the conditions under which a W=0 branch exists in these theories and explores their flow via Higgs mechanism, including detailed examples.

Findings

W=0 branch exists if and only if anomaly matching holds at the origin.

SO(13) with a spinor has a dynamically generated superpotential without anomaly matching.

Flow from SO(13) to SU(6) preserves the W=0 branch and anomaly matching.

Abstract

We study the low-energy dynamics of all N=1 supersymmetric gauge theories whose basic gauge invariant fields are unconstrained. This set includes all theories whose matter Dynkin index is less than the index of the adjoint representation. We study the dynamically generated superpotential in these theories, and show that there is a W=0 branch if and only if anomaly matching is satisfied at the origin. An interesting example studied in detail is SO(13) with a spinor, a theory with a dynamically generated W and no anomaly matching at the origin. It flows via the Higgs mechanism to SU(6) with a three-index antisymmetric tensor, a theory with a W=0 branch and anomaly matching at the origin.