The anomaly that was not meant IIB

Debray, Arun; Dierigl, Markus; Heckman, Jonathan J.; Montero, Miguel

doi:10.1002/prop.202100168

Cited by 36 publications

(54 citation statements)

References 128 publications

(301 reference statements)

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“…Some of the earlier works on the subject include [25,37,38]. For more recent examples of differential cohomology applications in formal high-energy physics that are of some relevance to this work see [13,[39][40][41][42][43][44][45][46][47][48]. In this paper differential cohomology will be used to refine the notion of dimensional reduction (or KK-reduction) of supergravity theories, with the goal of providing a precise treatment of the effect of torsion cohomology classes in the compactification manifold.…”

Section: A Differential Cohomology Refinement Of Dimensional Reductionmentioning

confidence: 99%

Symmetry TFTs from String Theory

Apruzzi¹,

Bonetti²,

García-Etxebarria³

et al. 2021

Preprint

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We determine the d + 1 dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for d-dimensional QFTs obtained by compactifying M-theory on a non-compact space X. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary ∂X of the space X. Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space ∂X, which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries. We apply this framework to 7d super-Yang Mills, where X = C 2 /Γ ADE , as well as the Sasaki-Einstein links of Calabi-Yau three-fold cones that give rise to 5d superconformal field theories. This M-theory analysis is complemented with a IIB 5-brane web approach, where we derive the SymTFTs from the asymptotics of the 5-brane webs. Our methods apply to both Lagrangian and non-Lagrangian theories, and allow for many generalisations.

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Section: A Differential Cohomology Refinement Of Dimensional Reductionmentioning

confidence: 99%

Symmetry TFTs from String Theory

Apruzzi¹,

Bonetti²,

García-Etxebarria³

et al. 2021

Preprint

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“…It is important to understand what (topological) degrees of freedom exist in the theory. The same question also arises in Type IIB string theory [DDHM21].…”

Section: Anomaly Cancellationmentioning

confidence: 84%

Global anomalies in 8d supergravity

Lee,

Yonekura

2022

Preprint

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We study gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds. Possible global gauge anomalies are classified by spin bordism groups Ω spin 9 (BG) which we determine by spectral sequence techniques, and we also identify their explicit generator manifolds. It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in 8d N = 1 supergravity theory, have anomalies. We discuss how a 2-form field, which also appears in supergravity, produces anomalies which cancel against these fermion anomalies in a certain class of supergravity theories. In another class of theories, the anomaly of the gravitino is not cancelled by the 2-form field, but by topological degrees of freedom. It gives a restriction on the topology of spacetime manifolds which is not visible at the level of differential-form analysis.

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“…To be a bit more precise, on the left we are indicating the spin-cobordism groups supplemented by a trivialisation of the global current αn . 5 The lower stringcobordism groups were listed in table 5 and those relevant for us here are…”

Section: Gauging the Global Symmetry Of ω Spinmentioning

confidence: 99%

“…Note that cobordism groups also play a prominent role in the computation of Dai-Freed anomalies, see e.g [4,5]…”

mentioning

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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The anomaly that was not meant IIB

Cited by 36 publications

References 128 publications

Symmetry TFTs from String Theory

Symmetry TFTs from String Theory

Global anomalies in 8d supergravity

Open-Closed Correspondence of K-theory and Cobordism

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