LargeNfield theory and AdS tachyons

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 doubletrace 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(λ), 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.

Perturbative realization of Miransky scaling

“…Both of these properties actually hold to all orders in perturbation theory in the Veneziano limit, as was shown in Ref. [40]. In Appendix A we provide the full N f -dependent beta functions to two loops.…”

On non-supersymmetric conformal manifolds: field theory and holography

“…It was shown in [31] that (unlike in the parent supersymmetric theory) conformal invariance is broken already at leading order in 1/N , by the logarithmic running of double-trace operators. This looks like a generic phenomenon which has been proposed in [32,33] to be related to the presence of tachyonic instabilities in the gravity dual [34]. 12 In this context, the only model we are aware of which evades this problem, is a non-tachyonic orientifold of Type 0B string theory, discussed in [36].…”

O(N) model in 4<d<6 : Instantons and complex CFTs

“…A simple argument for the exponential suppression of the imaginary parts is that on the sphere S d , or cylinder S d−1 × R, the conformal coupling to curvature adds a positive quadratic term to the scalar potential, making the perturbative vacuum metastable. We demonstrate the smallness of imaginary parts explicitly by computing, at large N , the sphere The fact that the imaginary parts are very small for large N , makes the O(N ) models in 4 < d < 6 similar to the robust examples [35][36][37][38][39][40][41][42] of complex CFTs corresponding to the walking RG flows and weakly first-order phase transitions. In d = 5, for large enough N the imaginary parts of scaling dimensions can be made so small that the numerical bootstrap studies cannot distinguish such complex CFTs from the regular CFTs.…”

“…, d + 1 and non-zero modes indexed by i: c a = (c A , c i ). If the coordinates v A parameterize the instanton moduli space, then 36) where N A is the norm of dσ/dv A . From c A ψ A = (dσ/dv A )dv A , we then conclude that dc A = √ N A dv A , and so the zero mode measure is…”