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Non-Invertible Symmetries in Supergravity

Eduardo García-Valdecasas

TL;DR

This work initiates the study of non-invertible p-form symmetries in the low-energy limits of M-theory and Type II string theories by leveraging ubiquitous Chern-Simons terms in supergravity. It constructs infinite families of topological defects in $11$-dimensional and $10$-dimensional supergravities via Page currents and higher gauging of discrete subgroups, and analyzes their action on probe branes. The authors discuss obstructions from higher anomalies and show that UV completion through dynamical branes explicitly breaks these non-invertible symmetries, strengthening the link between the absence of global symmetries in quantum gravity and the Completeness Hypothesis. The results provide a framework for non-invertible symmetries in string/M-theory and suggest a hierarchy of symmetry-breaking scales with potential implications for the Swampland and string compactifications.

Abstract

Non-invertible symmetries have been extensively studied in quantum field theories in recent years. In this note we initiate their study in supergravity. We find infinite families of non-invertible defects in 11d and 10d Type II supergravities. These operators display a rich action on different probe branes. We comment on how these symmetries are removed in the UV completion, M-theory and Type II String Theory and how their existence strengthens the link between the absence of global symmetries in Quantum Gravity and the Completeness Hypothesis.

Non-Invertible Symmetries in Supergravity

TL;DR

This work initiates the study of non-invertible p-form symmetries in the low-energy limits of M-theory and Type II string theories by leveraging ubiquitous Chern-Simons terms in supergravity. It constructs infinite families of topological defects in -dimensional and -dimensional supergravities via Page currents and higher gauging of discrete subgroups, and analyzes their action on probe branes. The authors discuss obstructions from higher anomalies and show that UV completion through dynamical branes explicitly breaks these non-invertible symmetries, strengthening the link between the absence of global symmetries in quantum gravity and the Completeness Hypothesis. The results provide a framework for non-invertible symmetries in string/M-theory and suggest a hierarchy of symmetry-breaking scales with potential implications for the Swampland and string compactifications.

Abstract

Non-invertible symmetries have been extensively studied in quantum field theories in recent years. In this note we initiate their study in supergravity. We find infinite families of non-invertible defects in 11d and 10d Type II supergravities. These operators display a rich action on different probe branes. We comment on how these symmetries are removed in the UV completion, M-theory and Type II String Theory and how their existence strengthens the link between the absence of global symmetries in Quantum Gravity and the Completeness Hypothesis.
Paper Structure (10 sections, 66 equations, 2 figures)

This paper contains 10 sections, 66 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Review of QFT examples
  3. Non-invertible symmetries in Supergravity
  4. 11d Supergravity
  5. Type IIA Supergravity
  6. Type IIB Supergravity
  7. A different approach
  8. Discussion
  9. The 7d $\mathbb{Z}_N$ TQFT
  10. Explicit construction of the non-invertible defects by half gauging

Figures (2)

  • Figure 1: A deformation of the naive operator $U_{\alpha} (\Sigma_3)$ generates an anomalous phase in the region swept by it.
  • Figure 2: A magnetic source for $F_4$ crosses the topological defect and picks up a fractional $F_4$ flux attached to it.