A Non-supersymmetric Deformation of the AdS/CFT Correspondence

TL;DR

This work implements a non-supersymmetric deformation of the AdS/CFT correspondence by introducing the scalar operator $O = \phi_1^2 + \phi_2^2 + \phi_3^2 + \phi_4^2 - 2 \phi_5^2 - 2 \phi_6^2$ into the ${\cal N}=4$ theory. The authors formulate a radial 5d gauged supergravity system with a single scalar $\lambda$ (via $\rho = e^{\lambda/\sqrt{6}}$) and explore its UV behavior, noting that a mass deformation corresponds to the nonzero $\mathcal{B}$ mode when $\lambda \sim \mathcal{A} e^{-\Delta r} + \mathcal{B} e^{-(4-\Delta)r}$ with $m^2 = \Delta(\Delta-4)$. They find that a supersymmetric first-order flow exists for certain branches but no global non-supersymmetric superpotential, requiring numerical solution of the second-order equations. The solution is then lifted to ten dimensions using the Pilch–Freed framework, yielding a consistent 10d background with a nontrivial metric and $F_{(5)}$ encoded through a function $w(r,\theta)$ and an auxiliary $F(r)$, with the Bianchi identity verified. Brane probing the 10d geometry confirms that the UV behavior encodes the intended mass operator, recovering the expected $m^2 e^{2r}$ scaling and yielding a flat potential in the supersymmetric limit; the full 10d lift reproduces the operator insertion, establishing a tractable non-supersymmetric gravity dual for this simple deformation.

Abstract

We deform the AdS/CFT Correspondence by the inclusion of a non-supersymmetric scalar mass operator. We discuss the behaviour of the dual 5 dimensional supergravity field then lift the full solution to 10 dimensions. Brane probing the resulting background reveals a potential consistent with the operator we wished to insert.