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The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland
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abstract
In this work we investigate the Swampland Cobordism Conjecture in the context of type IIB string theory geometries with non-trivial duality bundle. Quite remarkably, we find that many non-trivial bordism classes with duality bundles in Mp$(2,\mathbb{Z})$, a double cover of SL$(2,\mathbb{Z})$ related to fermions, correspond to asymptotic boundaries of well-known supersymmetric F-theory backgrounds. These include $[p,q]$-7-branes, non-Higgsable clusters, S-folds, as well as various lower-dimensional generalizations. These string theoretic objects break the global symmetries associated to the non-trivial bordism groups, providing a strong test of the Cobordism Conjecture. Further including worldsheet orientation reversal promotes the duality group to the Pin$^+$ cover of GL$(2,\mathbb{Z})$. The corresponding bordism groups require a new non-supersymmetric "reflection 7-brane" and its compactifications to ensure the absence of global symmetries, thus providing an interesting prediction of the Cobordism Conjecture for non-supersymmetric type IIB backgrounds. A major component of the present work is the explicit derivation of the involved bordism groups as well as their generators, which correspond to asymptotic boundaries of explicit string theory backgrounds. The main tool is the Adams spectral sequence, to which we provide a detailed introduction. We anticipate that the same techniques can be applied in a wide variety of settings.
Forward citations
Cited by 6 Pith papers
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The AdS/$\mathsf{C}$-$\mathsf{P}$-${\mathsf T}$ Correspondence
N=4 super Yang-Mills has P and T symmetries that mix with CP and CT under S-duality, and these map to specific worldsheet and geometric symmetries of Type IIB string theory.
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R7-branes and AdS$_{\text{9}}$ solutions in type IIB
Explicit analytic 7-brane solutions in type IIB are built with AdS9 near-horizon geometry, and imposing the reflection monodromy tau -> -bar tau selects a subclass proposed as R7-branes.
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Cobordism Utopia: U-Dualities, Bordisms, and the Swampland
For 8d maximal supergravity, the spin bordism groups Omega_k^Spin(B(SL(2,Z) x SL(3,Z))) for k=1..7 are computed and each generator is realized by a string/M/F-theory background, some of which are non-geometric.
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Gravitational Background of Alice-Vortices and R7-Branes
A family of asymptotic Alice-vortex/R7-brane backgrounds in axio-dilaton gravity is constructed, with the vortex tension encoded in a conical deficit and a generic intrinsic dipole moment.
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Non-supersymmetric branes and discrete topological terms
A direct computation from the tentative NS5-brane spectrum gives the opposite Z3 topological term (1/3 vs 2/3) from Tachikawa-Zhang, so the spectrum or the inflow interpretation must change.
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Relative Quantum Gravity: Localized Gravity and the Swampland
Localized gravity theories can violate swampland constraints, but satisfy them when defined relative to a higher-dimensional gravity completion, dubbed relative quantum gravity.
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