Anomaly Matching between Topological Superconductors and 𝒩=8 Supergravity
Abstract
The boundary of a 3+1-dimensional topological superconductor carries a ℤ16-valued global (Dai-Freed) anomaly, famously matched by the $16$ fermions of a Standard Model generation once a certain ℤ4 symmetry is gauged. In a supergravity completion, though, a gravitino contributes −7/16 rather than ±1/16, obstructing this ℤ4 in the Minimal Supersymmetric Standard Model. We observe that four-dimensional 𝒩=8 supergravity evades this fate. Its fermions, eight gravitini in the 8 and fifty-six spin-1/2 states in the 56=Λ38 of the SU(8) R-symmetry, cancel the anomaly. The cancellation holds for every admissible ℤ4 structure, is consistent with the vanishing of the continuous SU(8) anomaly, and follows from a Smith homomorphism and the Rarita-Schwinger ghost-subtraction weight identifying the supergravity anomaly with that of the topological superconductor. In maximal supergravity this ℤ4 stays anomaly-free and gaugeable despite its eight gravitini. All numbers are reproduced by an open-source library described in the Supplemental Material.
Related
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BibTeX
@misc{murphy2026anomaly,
title = {{Anomaly Matching between Topological Superconductors and $\mathcalN=8$ Supergravity}},
author = {Christopher W. Murphy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00214},
eprint = {2609.00214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00214},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Anomaly Matching between Topological Superconductors and 𝒩=8 Supergravity
AU - Christopher W. Murphy
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.00214
UR - https://arxiv.org/abs/2609.00214
AB - The boundary of a 3+1-dimensional topological superconductor carries a ℤ_16-valued global (Dai-Freed) anomaly, famously matched by the $16$ fermions of a Standard Model generation once a certain ℤ_4 symmetry is gauged. In a supergravity completion, though, a gravitino contributes −7/16 rather than ±1/16, obstructing this ℤ_4 in the Minimal Supersymmetric Standard Model. We observe that four-dimensional 𝒩=8 supergravity evades this fate. Its fermions, eight gravitini in the 8 and fifty-six spin-1/2 states in the 56=Λ^38 of the SU(8) R-symmetry, cancel the anomaly. The cancellation holds for every admissible ℤ_4 structure, is consistent with the vanishing of the continuous SU(8) anomaly, and follows from a Smith homomorphism and the Rarita-Schwinger ghost-subtraction weight identifying the supergravity anomaly with that of the topological superconductor. In maximal supergravity this ℤ_4 stays anomaly-free and gaugeable despite its eight gravitini. All numbers are reproduced by an open-source library described in the Supplemental Material.
ER -