Compactness of brane moduli and the String Lamppost Principle in d &gt; 6

Bedroya, Alek; Hamada, Yuta; Montero, Miguel; Vafa, Cumrun

doi:10.1007/jhep02(2022)082

Cited by 37 publications

(42 citation statements)

References 69 publications

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“…Let us point out that the Tameness Conjecture for field spaces also offers a more general perspective on the properties of brane moduli space. While for lower-dimensional branes these moduli spaces were conjectured to be compact [21,62], it is well-known that for higher-dimensional branes, such as 7-branes in Type IIB string theory compactness is not a suitable criterion. However, it is known from the geometric realization of 7-branes in an elliptically fibered Calabi-Yau manifold in F-theory that the moduli space of these extended objects is definable in an o-minimal structure.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Taming the Landscape of Effective Theories

Grimm¹

2021

Preprint

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We introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, we propose a Tameness Conjecture that states that all valid effective theories are labelled by a definable parameter space and must have scalar field spaces and coupling functions that are definable using the tame geometry built from an o-minimal structure. We give a brief introduction to tame geometry and describe how it restricts sets, manifolds, and functions.We then collect evidence for the Tameness Conjecture by studying various effective theories arising from string theory compactifications by using some recent advances in tame geometry.In particular, we will exploit the fact that coset spaces and period mappings are definable in an o-minimal structure and argue for non-trivial tameness results in higher-supersymmetric theories and in Calabi-Yau compactifications. As strongest evidence for the Tameness Conjecture over a discrete parameter space, we then discuss a recent theorem stating that the locus of self-dual flux vacua of F-theory admits a tame geometry even if one allows for any flux choice satisfying the tadpole constraint. This result implies the finiteness of self-dual flux vacua in F-theory.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Taming the Landscape of Effective Theories

Grimm¹

2021

Preprint

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“…Unfortunately, we are not aware of a proof of this behaviour and leave it for further study. 8 Gauging the global symmetry of Ω Spin 2 (pt)…”

Section: Breaking the Global Symmetry Of ωmentioning

confidence: 99%

Open-Closed Correspondence of K-theory and Cobordism

Blumenhagen,

Cribiori

2021

Preprint

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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 Spincobordisms and between K-groups and Spin c -cobordisms. We mainly focus on the case in which the global symmetries are eventually gauged and, by combining K-theory and cobordism, we recover tadpole cancellation conditions in type I string theory and F-theory from a purely bottom-up perspective. In the spirit of the swampland program, we provide a prescription to compute the relative normalisation between cobordism and K-theory charges in these tadpoles, without relying on string theory input.

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“…Low-energy interactions are fully determined by supersymmetry, to the point that the one free parameter in the theory is the number of vector multiplets at a generic point in moduli space, known as the rank of the theory [14,15]. Theories with 16 supercharges have been the subject of much recent work from the Swampland perspective [16][17][18][19][20][21], to the point that Swampland principles are enough to "bootstrap" the known string theory compactifications, realizing the String Lamppost Principle. In particular, there is an upper bound on the rank of the theory, which is 26 − d for a d-dimensional theory [22].…”

Section: Superchargesmentioning

confidence: 99%

“…Although the philosophy and many of the details are very similar to the case of sixteen supercharges, with eight supercharges we encounter, for the first time, a large landscape of solutions, related to the existence of a large number of Calabi-Yau manifolds. By contrast, minimally supersymmetric compactifications in d > 6 are all related to M theory on K3 [21], possibly with frozen singularities, which makes the number of possibilities very limited.…”

Section: Bps Mass Gap In 6d N =1 Eftsmentioning

confidence: 99%

The Desert and the Swampland

Long¹,

Vafa²,

Valenzuela³

2021

Preprint

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The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the "BPS desert conjecture", resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications.

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Compactness of brane moduli and the String Lamppost Principle in d > 6

Cited by 37 publications

References 69 publications

Taming the Landscape of Effective Theories

Taming the Landscape of Effective Theories

Open-Closed Correspondence of K-theory and Cobordism

The Desert and the Swampland

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