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The anomaly that was not meant IIB

Arun Debray, Markus Dierigl, Jonathan J. Heckman, Miguel Montero

TL;DR

The paper analyzes whether the discrete duality symmetry of Type IIB string theory, captured by the group $ ext{GL}^+(2,\mathbb{Z})$, can be gauged without quantum inconsistencies. By computing the 11d bordism group $ Omega_{11}^{\text{Spin-GL}^+(2,\mathbb{Z})}$ and the associated duality anomaly theory, the authors show nonvanishing anomalies in the textbook IIB setup, yet demonstrate cancellation via a subtle modification of the 10d Chern–Simons term that depends on the specific field content, as well as alternative topological Green–Schwarz mechanisms. The work also reveals a rich set of alternative IIB-like theories with the same low-energy supergravity but different extended-object spectra, raising swampland questions and the possibility of cobordism-domain walls connecting distinct UV completions. A particularly intricate case, Arcanum XI ($X_{11}$), remains inconclusive due to the lack of a canonical quadratic refinement on certain Spin-$\text{GL}^+(2,\mathbb{Z})$ manifolds. Overall, the results reinforce F-theory’s consistency while opening avenues for understanding discrete duality backgrounds, higher-form symmetries, and the global structure of the IIB landscape.

Abstract

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

The anomaly that was not meant IIB

TL;DR

The paper analyzes whether the discrete duality symmetry of Type IIB string theory, captured by the group , can be gauged without quantum inconsistencies. By computing the 11d bordism group and the associated duality anomaly theory, the authors show nonvanishing anomalies in the textbook IIB setup, yet demonstrate cancellation via a subtle modification of the 10d Chern–Simons term that depends on the specific field content, as well as alternative topological Green–Schwarz mechanisms. The work also reveals a rich set of alternative IIB-like theories with the same low-energy supergravity but different extended-object spectra, raising swampland questions and the possibility of cobordism-domain walls connecting distinct UV completions. A particularly intricate case, Arcanum XI (), remains inconclusive due to the lack of a canonical quadratic refinement on certain Spin- manifolds. Overall, the results reinforce F-theory’s consistency while opening avenues for understanding discrete duality backgrounds, higher-form symmetries, and the global structure of the IIB landscape.

Abstract

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

Paper Structure

This paper contains 24 sections, 10 theorems, 117 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Bordism groups and anomalies
  3. Duality in type IIB string theory
  4. Duality group of type IIB string theory
  5. Non-trivial duality backgrounds
  6. Duality anomalies of type IIB string theory
  7. The IIB anomaly theory
  8. Computation of the anomaly
  9. Physical interpretation and anomaly cancellation
  10. Alternative type IIB theories
  11. Cancellation via a topological Green-Schwarz mechanism
  12. Comment on congruence subgroups and the Swampland
  13. The manifold X11
  14. Conclusions and future directions
  15. Varying axio-dilaton and the SL2R anomaly
  16. ...and 9 more sections

Key Result

Theorem C.2

Let $c\in H^n(B';\mathbb{Z}_2)$ and suppose the corresponding class $Uc\in\widetilde{H}^n(M;\mathbb{Z}_2)$ is such that $\mathrm{Sq}^2\mathrm{Sq}^2\mathrm{Sq}^2(Uc)\ne 0$. Then there is an $n$-dimensional Spin-$B$ manifold $W$ with $\int_W c\ne 0$, and $W$ generates a $\mathbb{Z}_2$ summand of $\Ome

Figures (3)

  • Figure 1: We have found several seemingly consistent versions of type IIB theory with a non-anomalous duality group, which differ from each other at the level of massive states and extended objects. Perhaps some (or all) of these alternate versions are in the Swampland. But it does raise the question of whether the usual M-theory star picture should be replaced by a multi-sheeted one with different topological sectors. In that scenario we would expect all of these to be connected to each other via cobordism domain walls McNamara:2019rup.
  • Figure 2: Schematic picture of a bordism manifold between two bounding circles.
  • Figure 4: The Serre spectral sequence for the cohomology of $Q_4^{11}$. Left: $\mathbb{Z}$ coefficients. Right: $\mathbb{Z}_4$ coefficients. We will show the three indicated differentials vanish, which implies both spectral sequences collapse.

Theorems & Definitions (18)

  • Theorem C.2
  • Proposition C.7
  • proof
  • Lemma C.12
  • proof
  • Proposition D.29
  • proof
  • Proposition D.30
  • proof
  • Lemma D.34
  • ...and 8 more