Bordisms between 9d type IIB supergravities and commutator widths of duality groups
- 1Universidad de Valparaíso
- 2Theoretical Physics Department, CERN
Abstract
We study the topological properties of bordisms interpolating between different 9d gauged supergravities obtained from compactification of type IIB string theory on 𝕊1 with a non-trivial SL(2, ℤ) bundle. We describe how such bordisms implement the needed monodromies through stacks of [p, q] 7-branes or gravitational solitons of non-trivial topology. For the later mechanism, we see that the topology of the bordism becomes increasingly complicated for large monodromies, which results in the associated bordisms being arbitrarily suppressed, against expectations on the breaking of global symmetries in Quantum Gravity. Motivated by this, we propose a refinement of the Swampland Cobordism Conjecture for the first bordism group Ω1(BG) with a G duality bundle. We argue that even if gravitational solitons can realize the monodromies associated with elements of the commutator subgroup of G, if the number of needed commutators is unbounded (in other words, the commutator width of G diverges) then an infinite number of duality defects realizing elements in G need to be included. We test this proposal for different duality groups G, and see that our expectations are realized, often in non-trivial ways.
Related
BibTeX
@article{heras2026bordisms,
title = {{Bordisms between 9d type IIB supergravities and commutator widths of duality groups}},
author = {Camilo las Heras and Ignacio Ruiz},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)255},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)255},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Bordisms between 9d type IIB supergravities and commutator widths of duality groups
AU - Camilo las Heras
AU - Ignacio Ruiz
PY - 2026
DA - 2026/10/26
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)255
UR - https://link.springer.com/article/10.1007/JHEP10(2026)255
AB - We study the topological properties of bordisms interpolating between different 9d gauged supergravities obtained from compactification of type IIB string theory on 𝕊^1 with a non-trivial SL(2, ℤ) bundle. We describe how such bordisms implement the needed monodromies through stacks of [p, q] 7-branes or gravitational solitons of non-trivial topology. For the later mechanism, we see that the topology of the bordism becomes increasingly complicated for large monodromies, which results in the associated bordisms being arbitrarily suppressed, against expectations on the breaking of global symmetries in Quantum Gravity. Motivated by this, we propose a refinement of the Swampland Cobordism Conjecture for the first bordism group Ω1(BG) with a G duality bundle. We argue that even if gravitational solitons can realize the monodromies associated with elements of the commutator subgroup of G, if the number of needed commutators is unbounded (in other words, the commutator width of G diverges) then an infinite number of duality defects realizing elements in G need to be included. We test this proposal for different duality groups G, and see that our expectations are realized, often in non-trivial ways.
SN - 1029-8479
ER -