Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7

TL;DR

This paper proves that all regular half-BPS flux solutions in M-theory with specific symmetries and asymptotics are essentially unique, showing a rigidity of the M-Janus solution and ruling out other smooth deformations.

Contribution

The authors demonstrate the non-existence of smooth, multi-region solutions beyond the M-Janus solution, establishing a rigidity result for half-BPS flux solutions in M-theory.

Findings

All regular solutions reduce to multiple covers of the M-Janus solution.

No smooth deformations away from the M-Janus solution satisfy the constraints.

Rigidity contrasts with solutions having different asymptotics like AdS7 x S4.

Abstract

The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $AdS_7 \times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $AdS_4 \times S^7$ and $AdS_7 \times S^4$ asymptotic regions.