Dual of the Janus solution: An interface conformal field theory

Abstract

We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys. 05 (2003) 072]. The dual field theory is $\mathcal{N}=4$ SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator ${\mathcal{L}}^{\ensuremath{'}}$ which is the fourth descendent of the primary $\mathrm{T}\mathrm{r}{X}^{{I}{X}^{J}}$ and closely related to the $\mathcal{N}=4$ Lagrangian density. At the classical level supersymmetry is broken explicitly, but $SO(3,2)$ conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of ${g}_{YM}^{2}$, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value $⟨{\mathcal{L}}^{\ensuremath{'}}⟩$ are protected to all orders in ${g}_{YM}^{2}N$, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. $SO(3,2)$ symmetry requires vanishing vacuum energy, $⟨{T}_{\ensuremath{\mu}\ensuremath{\nu}}⟩=0$, and this is confirmed in first order in the discontinuity.