Maze topiary in supergravity

• Published in: The journal of high energy physics Vol. 2025; no. 3; pp. 120 - 46
• Main Authors: Bena, Iosif, Houppe, Anthony, Toulikas, Dimitrios, Warner, Nicholas P.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 14.03.2025; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Black holes; Black Holes in String Theory; Branes; Classical and Quantum Gravitation; Elementary Particles; Entropy; Event horizon; Gravity; High energy physics; High Energy Physics - Theory; M-Theory; Momentum; Monge-Ampere equation; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Riemann surfaces; String Theory; Supergravity; Symmetry; Black Holes in String Theory; M-Theory; horizon; anti-de Sitter; supergravity, solution; membrane model; black hole, entropy; BTZ; geometry; warped; nonlinear; Riemann surface; duality
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP03(2025)120

A bstract We show that the supergravity solutions for 1 4 -BPS intersecting systems of M2 and M5 branes are completely characterized by a single “maze” function that satisfies a non-linear “maze” equation similar to the Monge-Ampère equation. We also show that the near-brane limit of certain intersections are AdS 3 ×S 3 ×S 3 solutions warped over a Riemann surface, Σ. There is an extensive literature on these subjects and we construct mappings between various approaches and use brane probes to elucidate the relationships between the M2-M5 and AdS systems. We also use dualities to map our results onto other systems of intersecting branes. This work is motivated by the recent realization that adding momentum to M2-M5 intersections gives a supermaze that can reproduce the black-hole entropy without ever developing an event horizon. We take a step in this direction by adding a certain type of momentum charges that blackens the M2-M5 intersecting branes. The near-brane limit of these solutions is a BTZ extremal ×S 3 ×S 3 × Σ geometry in which the BTZ momentum is a function of the Riemann surface coordinates.