BPS solution for eleven-dimensional supergravity with a conical defect configuration

TL;DR

This paper derives a BPS solution in eleven-dimensional supergravity featuring a conical defect, analyzing its properties and potential applications in condensed matter physics.

Contribution

It presents a new exact solution for supergravity with a conical defect linked to a brane tension, including the near-horizon geometry analysis.

Findings

Found a full solution for supergravity with a conical defect.

Demonstrated the near-horizon limit yields an $AdS_4 imes S^1 imes ext{E}^6$ geometry.

Discussed potential applications in strong coupling condensed matter systems.

Abstract

In this work, we found the solution for the field equations of eleven-dimensional supergravity with a BPS conical topological defect configuration. We chose the solutions that corresponded to a M2-brane where the space-time presents the co-dimension two. The source of the topological defect is a sigma model where the brane tension is connected with the angular deficit. We analyzed the Killing spinor equations, a 3-form gauge potential and Einstein's equations, proving that it is possible to find a full solution for the system. We analyzed the near-horizon limit proving that it is possible to obtain an $AdS_4 \times S^1 \times \mathbb{E}^6 $ geometry for certain values of the brane tension. We also discussed some applications in the strong coupling theory for condensed matter systems.