Non-Invertible Symmetries in Compactified Supergravities

TL;DR

This paper investigates how non-invertible higher-form symmetry defects in eleven-dimensional supergravity descend to Type IIA supergravity through Kaluza--Klein compactification, revealing new structures in the defect algebra.

Contribution

It demonstrates the explicit descent of non-invertible supergravity defects from eleven to ten dimensions, including the auxiliary sectors and their algebraic structures.

Findings

Full defect including auxiliary sectors admits a pushforward along the M-theory circle.

The auxiliary theory descends from a seven-dimensional Chern--Simons-like sector to a six-dimensional BF-type sector.

Type IIA defect algebra contains both invertible and non-invertible sectors, with charged probes identified via brane dictionary.

Abstract

We study the \textit{Kaluza--Klein} descent of non-invertible higher-form symmetry defects from eleven-dimensional Supergravity to Type IIA Supergravity. Starting from the eleven-dimensional construction of non-invertible Supergravity defects, we show that the full defect, including its auxiliary topological sector, admits a pushforward along the M-theory circle in the zero-mode Supergravity regime. The seven-dimensional \textit{Chern--Simons}-like auxiliary theory descends to a six-dimensional \(BF\)-type sector. We also show that the compactification of the eleven-dimensional \textit{Bianchi} sector splits into an invertible \(H_{[3]}\)-sector and a twisted non-invertible \(\widetilde F_{[4]}\)-sector, controlled by \(d\widetilde F_{[4]}+H_{[3]}\wedge F_{[2]}=0\). The resulting Type IIA defect algebra contains both an invertible Picard subgroup and non-invertible \(BF\)-dressed defects, with charged probes identified through the standard M-theory/Type IIA brane dictionary.