Central Charges and $U(1)_R$ Symmetries in ${\cal N}=1$ Super Yang-Mills

TL;DR

This paper investigates the phase structure of ${ m ext{SU}}(N_c)$ ${ m ext{N}}=1$ super Yang-Mills theory with matter fields, providing insights into the behavior of the central charge $a$ during renormalization group flows.

Contribution

It applies recent theoretical results to analyze the phase structure and supports the conjecture that the central charge $a$ decreases along RG flows in ${ m ext{N}}=1$ super Yang-Mills theories.

Findings

Supports the conjecture that $a$ decreases under RG flows.

Provides a detailed analysis of phase structure with matter fields.

Confirms that $a$ is non-negative in unitary 4D conformal field theories.

Abstract

We use recent results of Intriligator and Wecht [hep-th/0304128] to study the phase structure of $\NN=1$ super Yang-Mills theory with gauge group $SU(N_c)$, a chiral superfield in the adjoint, and $N_f$ chiral superfields in the fundamental representation of the gauge group. Our discussion sheds new light on [hep-th/0304128] and supports the conjecture that the central charge $a$ decreases under RG flows and is non-negative in unitary four dimensional conformal field theories.