Exact half-BPS type IIB interface solutions I: local solution and supersymmetric Janus

Abstract

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS 4 × S 2 × S 2 × Σ with SO(2, 3) × SO(3) × SO(3) symmetry in terms of two holomorphic functions on a Riemann surface Σ, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS 5 × S 5 and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper [1]. 2 The bulk Lagrangian may be put in a more standard from by scaling the scalar fields asφ i → g −2φi at the cost of introducing interface operators of the form (∂ π g) 2φiφj .6

Three-dimensional N = 4 $$ \mathcal{N}=4 $$ linear quivers and non-Abelian T-duals

“…Following the formulation initiated in [61,62], the authors of [58,60] proposed that the supergravity solutions associated to the three dimensional N = 4 CFTs that we just described are fibrations of AdS 4 × S 2 × S 2 over a Riemann surface Σ 2 . We will refer to these geometries as ABEG geometries for brevity.…”

“…Notice that we are working in string frame, hence some factors of the dilaton differ from [60,62], which use Einstein frame. Finally, the 1-form f is given by,…”

“…The brane distribution is depicted in figure 3. The Laplace problem that these functions solve must be complemented by conditions on the boundaries of the Riemann surface [61,62],…”

Gravity and on-shell probe actions

“…A particularly interesting framework is provided by the "bubbling geometries" obtained in [69][70][71][72][73][74]. 35 For instance, one can consider geometries dual to half-BPS Wilson loops of the N = 4 super Yang-Mills theory in large representations of the gauge group SU(N ), with Young tableaux containing of the order of N 2 boxes.…”

Band structure in Yang-Mills theories

“…The W m are examples of boundary or interface operators (also called Janus interfaces when they carry no degrees of freedom, as in this case). They have been studied extensively in N = 4 super Yang-Mills where they preserve space-time supersymmetry if combined with an appropriate discontinuity of the coupling g [22,23]. More generally, these interfaces can be conformal but not topological as should be clear from the fact that they modify operator dimensions (for a recent discussion of the θ-dependence of scaling dimensions in N = 4 super Yang-Mills see [24]).…”