Perturbative Search for Fixed Lines in Large N Gauge Theories

TL;DR

This paper investigates the existence of fixed lines in the coupling space of large N gauge theories derived from orbifolds of N=4 SYM, finding no such lines in non-supersymmetric cases and discussing implications for string theory.

Contribution

It provides a general method to determine fixed lines in large N gauge theories and applies it to orbifolds, highlighting the absence of fixed lines in non-supersymmetric examples.

Findings

No large N non-supersymmetric theories with fixed lines passing through the origin.

Decoupling of U(1) factors is crucial in the analysis.

Connection to closed string tachyon condensation is discussed.

Abstract

The logarithmic running of marginal double-trace operators is a general feature of 4-d field theories containing scalar fields in the adjoint or bifundamental representation. Such operators provide leading contributions in the large N limit; therefore, the leading terms in their beta functions must vanish for a theory to be large N conformal. We calculate the one-loop beta functions in orbifolds of the N=4 SYM theory by a discrete subgroup Gamma of the SU(4) R-symmetry, which are dual to string theory on AdS_5 x S^5/Gamma. We present a general strategy for determining whether there is a fixed line passing through the origin of the coupling constant space. Then we study in detail some classes of non-supersymmetric orbifold theories, and emphasize the importance of decoupling the U(1) factors. Among our examples, which include orbifolds acting freely on the S^5, we do not find any large N non-supersymmetric theories with fixed lines passing through the origin. Connection of these results with closed string tachyon condensation in AdS_5 x S^5/Gamma is discussed.