Large N Field Theory and AdS Tachyons

TL;DR

This paper investigates the relationship between double-trace operator running in non-supersymmetric orbifolds of N=4 super Yang-Mills and tachyonic instabilities in AdS_5, establishing a precise duality and analyzing conformal symmetry breaking.

Contribution

It provides a detailed field theory derivation of the double-trace beta function and links it to bulk tachyonic modes, extending the AdS/CFT correspondence to non-supersymmetric large N theories.

Findings

Double-trace beta function is quadratic in coupling at all orders.

Conformal dimensions can become complex at fixed points, indicating instability.

Conformal invariance is broken if and only if dynamical symmetry breaking occurs.

Abstract

In non-supersymmetric orbifolds of N =4 super Yang-Mills, conformal invariance is broken by the logarithmic running of double-trace operators -- a leading effect at large N. A tachyonic instability in AdS_5 has been proposed as the bulk dual of double-trace running. In this paper we make this correspondence more precise. By standard field theory methods, we show that the double-trace beta function is quadratic in the coupling, to all orders in planar perturbation theory. Tuning the double-trace coupling to its (complex) fixed point, we find conformal dimensions of the form 2 + i b, as formally expected for operators dual to bulk scalars that violate the stability bound. We also show that conformal invariance is broken in perturbation theory if and only if dynamical symmetry breaking occurs. Our analysis is applicable to a general large N field theory with vanishing single-trace beta functions.