[Paper Review] Non-Supersymmetric Conformal Field Theories from Stable Anti-de Sitter Spaces

Jacques Distler, Frederic Zamora|ArXiv.org|Oct 26, 1998

Black Holes and Theoretical Physics16 references15 citations

TL;DR

This paper constructs non-supersymmetric conformal field theories (CFTs) in 3D and 4D via the CFT/AdS correspondence by deforming known supersymmetric CFTs with relevant operators. It demonstrates that the resulting anti-de Sitter backgrounds are stable only in specific cases—such as SU(3) invariant deformations—while SO(5) and other deformations lead to unstable backgrounds, ruling out corresponding CFTs.

ABSTRACT

We describe new non-supersymmetric conformal field theories in three and four dimensions, using the CFT/AdS correspondence. In order to believe in their existence at large N_c and strong 't Hooft coupling, we explicitly check the stability of the corresponding non-supersymmetric anti-de Sitter backgrounds. Cases of particular interest are the relevant deformations of the N=4 SCFT in SU(3) and SO(5) invariant directions. It turns out that the former is a stable, and the latter an unstable non-supersymmetric type IIB background.

Motivation & Objective

• To construct new non-supersymmetric conformal field theories in 3D and 4D using the CFT/AdS correspondence.
• To verify the stability of non-supersymmetric anti-de Sitter backgrounds resulting from relevant deformations of supersymmetric CFTs.
• To determine whether such stable backgrounds correspond to well-defined infrared fixed points in the dual field theory.
• To analyze the mass spectrum and stability of supergravity solutions arising from R-symmetry-breaking deformations of N=4 SYM and N=(2,0) SCFT.
• To assess the viability of non-supersymmetric M-theory and type IIB backgrounds in constructing new CFTs in higher dimensions.

Proposed method

• Uses the CFT/AdS correspondence to map relevant perturbations in the boundary CFT to scalar deformations in the bulk supergravity.
• Applies the 5D N=8 SU(4) gauged supergravity Lagrangian to study RG flows from N=4 SYM with gaugino mass or scalar mass terms.
• Performs linearized fluctuation analysis on the supergravity background to compute the mass spectrum of scalar and metric modes.
• Evaluates the stability of the background by checking whether scalar modes violate the Freedman-Breitenlohner bound (m² ≥ -9 in AdS₅, m² ≥ -24 in AdS₇).
• Analyzes the traceless and trace modes of metric fluctuations on S²×S² in M-theory backgrounds to identify breathing modes with negative mass-squared.
• Diagonalizes mixed scalar mass terms arising from volume-preserving and volume-changing fluctuations in the 11D supergravity action.

Experimental results

Research questions

• RQ1 Can non-supersymmetric CFTs in 3D and 4D be consistently constructed via relevant deformations of supersymmetric CFTs using the CFT/AdS correspondence?
• RQ2 Does the SU(3) invariant deformation of N=4 SYM lead to a stable non-supersymmetric AdS₅ background?
• RQ3 Is the SO(5) invariant deformation of N=4 SYM in 4D also stable, and does it yield a valid infrared CFT?
• RQ4 Does the deformation of the 6D N=(2,0) SCFT breaking SO(5) R-symmetry to SO(4) lead to a stable M-theory background?
• RQ5 Is the non-supersymmetric AdS₇×S²×S² M-theory background stable, and does it correspond to a consistent 6D CFT?

Key findings

• The SU(3) invariant deformation of N=4 SYM leads to a stable non-supersymmetric AdS₅×S̃⁵ background, confirming the existence of a new non-supersymmetric 4D CFT.
• The SO(5) invariant deformation of N=4 SYM results in an unstable supergravity background due to a tachyonic breathing mode with m² = -24, violating the stability bound.
• The non-supersymmetric M-theory background AdS₇×S²×S² is unstable, as the lowest breathing mode has m² = -24, below the critical bound of m² ≥ -24 in AdS₇.
• The mass spectrum of the SU(3) background shows no tachyonic modes, confirming its stability and consistency as a supergravity solution.
• The analysis reveals that the scalar modes in the S²×S² background have mixed mass terms requiring diagonalization, and the breathing mode is the primary instability source.
• The paper corrects an earlier error in applying curvature tensor formulas from prior work, showing that the standard form R_{κλμν} ∝ (g_{κμ}g_{λν} - g_{κν}g_{λμ}) does not hold for product spaces like S²×S².