Anomaly Inflow and p-Form Gauge Theories

Hsieh, Chang-Tse; Tachikawa, Yuji; Yonekura, Kazuya

doi:10.1007/s00220-022-04333-w

Cited by 45 publications

(111 citation 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%

“…This formalism is particularly useful to keep track of subtler aspects that emerge when we consider spacetimes with non-trivial topology (and in particular with torsional cycles). We refer the reader to [24,25,45,[60][61][62] for reviews aimed at physicists. We also highly recommend the textbook by Bär and Becker [63] for a pedagogical discussion of most of the results below.…”

Section: Aspects Of Differential Cohomologymentioning

confidence: 99%

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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%

Section: Aspects Of Differential Cohomologymentioning

confidence: 99%

Symmetry TFTs from String Theory

Apruzzi¹,

Bonetti²,

García-Etxebarria³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…where in our case A depends on the η-invariants for the gravitini and dilatini, as well as a slight extension of the anomaly theory of the chiral 4-form of type IIB supergravity developed in [21,[25][26][27]. Specifically, the anomaly theory relies on the existence of a canonical choice for the quadratic refinement of the pairing in differential cohomology, a feature which has only been shown to exist for Spin manifolds without a duality bundle turned on; in this paper, we assume that such a canonical choice exists for general Spin-GL + (2, Z) manifolds.…”

Section: Introductionmentioning

confidence: 99%

“…Still, to our knowledge, there has been no direct verification of this important feature (see however [19,20] which discuss a related anomaly). One obstacle in performing such a computation is that the evaluation of the partition function requires a detailed understanding of the self-dual field, and this has only recently been accomplished [21] (see also [22][23][24][25][26][27][28]).…”

Section: Introductionmentioning

confidence: 99%

The anomaly that was not meant IIB

Debray,

Dierigl,

Heckman

et al. 2021

Preprint

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Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

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“…Following the argument in[30,39], we assume that there is no half-integral contribution to the flux quantization condition as far as the setup in this paper in concerned.…”

mentioning

confidence: 99%

M5-branes Probing Flux Backgrounds

Bah¹,

Bonetti²,

Leung³

et al. 2021

Preprint

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We analyze the global symmetries and anomalies of 4d N = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved C 2 /Z k singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G 4 -flux configuration labeled by a collection of 2(k − 1) flux quanta, {N i }. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS 5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the 't Hooft anomalies for continuous symmetries at leading order in the limit of large N , N i . Contents 1 Introduction and summary 1 2 Geometric setup 4 2.1 Orbifold action and resolution of singularities 4 2.2 Topological twists 6 2.3 Homology of M 6 and sum rules 7 3 Continuous and discrete flavor symmetries 11 4 Inflow anomaly polynomial 13 4.1 Anomaly inflow methods for wrapped M5-branes 13 4.2 Construction of E 4 15 4.3 Integrating out massive fields 15 4.4 Results for continuous symmetries 16 4.5 Parity symmetries 19 5 Conclusion 20 A Resolution of S 4 /Z k orbifold singularities 21 B Cohomology class representatives of M 6 23 C The full inflow anomaly polynomial 32 D Basis-(in)dependence of the anomaly polynomial 35

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Anomaly Inflow and p-Form Gauge Theories

Cited by 45 publications

References 113 publications

Symmetry TFTs from String Theory

Symmetry TFTs from String Theory

The anomaly that was not meant IIB

M5-branes Probing Flux Backgrounds

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