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 $AdS_4 \times S^2 \times S^2 \times \Sigma$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $\Sigma$, 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.

• The paper derives exact half-BPS Type IIB solutions by reducing BPS equations using SO(2,3)×SO(3)×SO(3) symmetry.
• It maps the BPS equations to an integrable system resembling Liouville and sine-Gordon theories via two holomorphic functions.
• It identifies a non-singular supersymmetric Janus solution that serves as the holographic dual of a maximally supersymmetric Yang-Mills interface.

Review of the Paper: "Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus"

The paper discusses the derivation of complete Type IIB supergravity solutions with 16 supersymmetries, focusing on configurations with an $AdS_4 \times S^2 \times S^2 \times \Sigma$ geometry. These solutions present $SO(2,3) \times SO(3) \times SO(3)$ symmetry and are defined in terms of two holomorphic functions on a Riemann surface $\Sigma$. The authors identify a particular non-singular solution, termed the supersymmetric Janus solution, which serves as a holographic dual to a maximally supersymmetric Yang-Mills interface theory. This paper lays the groundwork for constructing globally non-singular solutions with interesting theoretical implications for the AdS/CFT correspondence.

Summary of Key Contributions

1. Symmetry Reduction and BPS Equations: The research provides the exact solutions by reducing the BPS equations using the $SO(2,3) \times SO(3) \times SO(3)$ symmetry. The authors demonstrate that the resulting BPS equations solve the full Type IIB supergravity field equations.
2. Mapping to Integrable Systems: The BPS equations are transformed into a new integrable system, resembling Liouville and Sine-Gordon theories. This integrable system is further mapped onto a linear equation, allowing for an exact solution utilizing two arbitrary holomorphic functions.
3. Identification of Solutions: Among infinite classes of solutions, they identify a non-singular Janus solution that is proposed as the AdS/CFT dual to the interface Yang-Mills theory with 16 supersymmetries, distinguishing itself by stability and preserved internal symmetry.

Implications and Future Directions

The construction of the supersymmetric Janus solution with 16 supersymmetries provides a new landscape for exploring the AdS/CFT correspondence in non-trivial interface CFTs. Beyond theoretical interest, these solutions could offer insights into the dualities involving conformal interfaces and defects.

The findings suggest several future research paths:

• Extension to Non-Singular Globally Solutions: A companion paper aims to explore these solutions further, including globally non-singular configurations and solutions doped with D5 and NS5 branes. This extension would enhance the understanding of how such configurations interact with each other in the string theory context.
• Applications in Gauge/Gravity Duality: The dual Conformal Field Theories that correspond to these gravitational solutions could be paved the way for studying field theories with interface or boundary conditions, determining how physical phenomena manifest in these dualities.
• Probes and Singularities: Investigation of the singularities like D5 and NS5 brane singularities would also lead to comprehending the landscape of stability and physical relevance of these solutions within the framework of holography.

The paper consolidates foundational methods for analyzing half-BPS geometries in supergravity, contributing significantly to the fields of mathematical physics and string theory by intertwining complex geometry, integrable systems, and theoretical physics. As the results do not rely on recent developments, they maintain a timeless quality that will support ongoing inquiries into higher-dimensional supergravity solutions and their associated CFT duals.