ADS/CFT String Duality and Conformal Gauge Field Theories

TL;DR

This paper explores the duality between string theory on specific backgrounds and conformal gauge theories, deriving conditions for conformality at finite N and broken supersymmetry, with implications for various orbifold embeddings.

Contribution

It derives two-loop conformal constraints for non-supersymmetric gauge theories from string compactifications, extending the understanding of AdS/CFT correspondence beyond supersymmetric cases.

Findings

Two-loop conformal conditions for non-supersymmetric theories

Constraints on orbifold embeddings within the string background

Implications for finite N gauge theories

Abstract

Compactification of Type IIB superstring on an $AdS_5 \times S^5/\Gamma$ background leads to SU(N) gauge field theories with prescribed matter representations. In the 't Hooft limit of large N such theories are conformally finite. For finite N and broken supersymmetry ($\cal N$ = 0) I derive the constraints to be two-loop conformal and examine the consequences for a wide choice of $\Gamma$ and its embedding $\Gamma \subset {\cal C}^3 (\supset S^5)$.