Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus

TL;DR

This work constructs the complete local set of half-BPS Type IIB supergravity solutions with AdS4×S2×S2×Σ geometry and SO(2,3)×SO(3)×SO(3) symmetry, expressing all fields in terms of two holomorphic data on Σ. It reveals that the reduced BPS system is integrable, and through a sequence of variable changes maps to a linear problem governed by two harmonic functions h1 and h2 on Σ, enabling explicit, globally regular solutions. Among these, a regular Half-BPS Janus solution is identified, providing the holographic dual to the maximally supersymmetric interface Yang-Mills theory; the paper also outlines plans for companion work to obtain fully back-reacted AdS5×S5 and D5/NS5-doped Janus solutions. The approach unifies geometric reduction, integrable-system techniques, and holographic interpretation to illuminate interface physics in highly supersymmetric settings. The results set the stage for constructing a broader class of globally non-singular, back-reacted geometries and their AdS/CFT duals in subsequent work.

Abstract

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times Σ$ with $SO(2,3) \times SO(3) \times SO(3)$ 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 $AdS_5 \times S^5$ and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.

Figures (3)

• Figure 1: Three-dimensional plot of the dilaton $e^{4\phi}$ (left) and the metric factor $f_{4}^{2}$ (right) for the supersymmetric Janus solution as a function of $x$ and $y$, for $r=4$.
• Figure 2: Three-dimensional plot of the metric factor $f_{1}^{2}$ and $f_{2}^{2 }$ for the supersymmetric Janus solution as function of $x$ and $y$, for $r=4$.
• Figure 3: Plot of the dilaton $e^{4\phi}$ at $y=0$ as a function of $x$, for $r=1.5$ (blue), $r=2$ (red), $r=3$ (magenta) and $r=4$ (green).