M/F-Theory as Mf-Theory

Sati, Hisham; Schreiber, Urs

doi:10.48550/arxiv.2103.01877

Cited by 4 publications

(8 citation statements)

References 55 publications

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“…Hence, one might expect a notion of H-twisted cobordism classes, as well. There have been proposals for cobordism groups relevant for the heterotic string (Ω string n ) or even M-theory (Ω pin + n , but see also the recent proposal [16,18], similar in spirit to our analysis). It would be interesting to generalize our analysis to these theories as well.…”

Section: Discussionsupporting

confidence: 77%

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Open-closed correspondence of K-theory and cobordism

Blumenhagen

Cribiori

2022

J. High Energ. Phys.

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Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, which can be considered as the physical manifestation of a generalisation of the classic Conner-Floyd isomorphism. The picture is exemplified by the relations between KO-groups and Spin-cobordisms and between K-groups and Spinc-cobordisms. We suggest that global symmetries related by such an isomorphism are generically gauged. Indeed, by combining non-torsion K-theory and cobordism groups, we recover tadpole cancellation conditions well known from type I string theory and F-theory. For torsion charges, another possibility opens up.

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Section: Discussionsupporting

confidence: 77%

“…The type IIA case is not yet understood 5. Recently, in[16] charge quantisation in M-theory has been related to cobordism. This is further motivated by several non-trivial consistency checks[17][18][19].…”

mentioning

confidence: 99%

Open-closed correspondence of K-theory and cobordism

Blumenhagen

Cribiori

2022

J. High Energ. Phys.

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“…We discuss this in §2.5. See [Sa13][FSS19c][FSS19b] [SS21] for extensive discussion about the importance of the quaternionic Hopf fibration in the context of M-theory.…”

Section: Algebraic Topology/fieldsmentioning

confidence: 99%

“…As also indicated below in §2.5, the quaternionic Hopf fibration h H over S 4 ∼ = HP 1 plays a central role in describing the field strengths on the M-theory side in [Sa13][FSS19c][FSS19b], while quaternionic orientation using HP ∞ (and its finite-dimensional stabilizations in low dimensions) are central to the constructions in [SS21]. Rationally, since π i (HP ∞ ) ∼ = π i−1 (S 3 ) is torsion for i > 4, we have a rational equivalence HP ∞ Q ≃ K(Q, 4), and the Postnikov tower of HP ∞ looks like (with only main/relevant stages indicated)…”

Section: M-theory Dynamics and S 4 Via Hypothesis Hmentioning

confidence: 99%

Mysterious Triality and Rational Homotopy Theory

Sati¹,

Voronov²

2021

Preprint

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Mysterious duality has been discovered by Iqbal, Neitzke, and Vafa [INV02] as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E k .It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives rise to the same E k symmetry pattern. We present a sequence of topological spaces, starting with the four-sphere S 4 , and then forming its iterated cyclic loop spaces L k c S 4 , within which we discover the E k symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its E k symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space L k c S 4 is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of (11 − k)-dimensional supergravity as the defining equations of the Sullivan minimal model of L k c S 4 . This gives an explicit duality between algebraic topology and physics.Thereby, we extend Iqbal-Neitzke-Vafa's mysterious duality between algebraic geometry and physics into a triality, also involving algebraic topology. Via this triality, duality between physics and mathematics is demystified, and the mystery is transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. Now the question is: is there an explicit relation between the del Pezzo surfaces B k and iterated cyclic loop spaces of S 4 which would explain the common E k symmetry pattern?

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“…Indeed, even if the conjecture is quite recent, already a number of works appeared studying some of its aspects and consequences, including [5][6][7][8][9][10][11]. Bordisms are relevant in several areas in mathematics and physics, a nonexhaustive list of related works is [12][13][14][15][16] for anomalies, [17,18] in relation to bubbles of nothing, [19] for the conjecture in a holographic context, [20] about "Hypothesis H" on charge quantisation in M-theory. An introduction to some of the mathematical material, in a physical context, can be found e. g. in [21,22], that appeared prior to [4].…”

Section: Introductionmentioning

confidence: 99%

Looking for structure in the cobordism conjecture

2022

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The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.

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M/F-Theory as Mf-Theory

Cited by 4 publications

References 55 publications

Open-closed correspondence of K-theory and cobordism

Open-closed correspondence of K-theory and cobordism

Mysterious Triality and Rational Homotopy Theory

Looking for structure in the cobordism conjecture

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