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Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics

L. Girardello, M. Petrini, M. Porrati, A. Zaffaroni

TL;DR

The paper leverages the AdS/CFT correspondence to analyze marginal and relevant perturbations of $N=4$ SYM at large $N$. It shows the existence of two non-supersymmetric $AdS_5$ vacua in 5D $N=8$ gauged supergravity, interpreted as IR fixed points, and constructs interpolating RG-flow solutions that connect them to the UV $N=4$ theory, accompanied by a holographic $c$-function that increases toward the UV. It also demonstrates linearized, marginal deformations associated with $Y_{ijk}$ that preserve $N=2$ supersymmetry, providing evidence for a moduli space of $N=1$ fixed points within the supergravity approximation. Together, these results map concrete supergravity scalars to field-theory mass terms and organize the operator content and flows at large $N$, offering a framework to discuss otherwise inaccessible IR conformal theories and their spectra.

Abstract

We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large $N$ limit. We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments.

Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics

TL;DR

The paper leverages the AdS/CFT correspondence to analyze marginal and relevant perturbations of SYM at large . It shows the existence of two non-supersymmetric vacua in 5D gauged supergravity, interpreted as IR fixed points, and constructs interpolating RG-flow solutions that connect them to the UV theory, accompanied by a holographic -function that increases toward the UV. It also demonstrates linearized, marginal deformations associated with that preserve supersymmetry, providing evidence for a moduli space of fixed points within the supergravity approximation. Together, these results map concrete supergravity scalars to field-theory mass terms and organize the operator content and flows at large , offering a framework to discuss otherwise inaccessible IR conformal theories and their spectra.

Abstract

We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large limit. We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments.

Paper Structure

This paper contains 5 sections, 38 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Spectrum of Type IIB on $AdS_5 \times S^5$
  3. Gauged N=8 Supergravity in Five Dimensions and Relevant Perturbations
  4. The Renormalization Group Flow
  5. Marginal Deformations of N=4 Super Yang Mills in the Supergravity Limit

Figures (4)

  • Figure 1: KK scalar states with zero or negative mass square. Supersymmetry multiplets correspond to vertical lines. Filled circles are associated with the states in the graviton multiplet. The $SU(4)$ representation of each scalar is indicated, together with the space-time field whose harmonic expansion gives rise to the particular state.
  • Figure 2: Shape of the $SO(5)$-symmetric upside-down potential $-V(\lambda)$; units on the coordinate axis are conventional
  • Figure 3: Shape of the $SU(3)\times U(1)$-symmetric upside-down potential $-V(\lambda)$
  • Figure 4: Products of harmonics in the fermion variations are decomposed into $SU(4)$ representations. Representations that contain the $4$ or $16$ of $SO(5)$ and can, therefore, contribute to the expansion into harmonics of the fermion shifts are indicated. The reduction to $SU(3)$ is obtained by splitting the indices of the $\underline{4}$ into $i=1,2,3$ and $4$, and by putting the index $4$ in all the relevant boxes. The representations that contains a $\underline{10}$ of $SU(3)$ are encircled.