The anomaly field theories of six-dimensional $(2,0)$ superconformal theories

Monnier, Samuel

doi:10.4310/atmp.2018.v22.n8.a6

Cited by 33 publications

(56 citation statements)

References 37 publications

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“…The technology that we developed above is not restricted to ALE cases, and applies equally well to any IIB background such that the horizon manifold is smooth. 15 We will 15 In some cases the IIB axio-dilaton might have non-trivial behaviour at infinity, so K-theory is not necessarily the right framework for classifying fluxes. (We refer the reader to [49] for a review of some of the difficulties in trying to extend the K-theory classification to situations in which SL(2, Z) dualities are important.)…”

Section: The Defect Group and The Linking Pairingmentioning

confidence: 99%

“…28 It should in principle be possible to compute this change in the partition function of IIB string theory in terms of an eleven-dimensional anomaly theory A (see [31,[64][65][66][67]) on a cylinder with boundary the ten dimensional configurations related by the large diffeomorphism. A natural stepping stone towards the full eleven-dimensional computation would be to reproduce the anomalous phases of the partition function from the behaviour of the anomaly theory for the six-dimensional (2, 0) theory [15]. See [59] for an analysis following this approach for the abelian case (or more generally, for six-dimensional theories with an invertible anomaly theory).…”

Section: Fractional Instanton Numbers and The Linking Formmentioning

confidence: 99%

“…) We emphasize that our viewpoint here, focusing purely on a careful analysis of the original construction of (2, 0) theories in ten dimensional type IIB string theory, is complementary to existing viewpoints on the partition function of (2, 0) theories. One such viewpoint is that of relative QFTs articulated by Freed and Teleman in [12], where one views the (2, 0) theories as furnishing the boundary degrees of freedom for certain non-invertible seven dimensional TQFTs [13][14][15]. For the A N cases one can also study the question using holography [16].…”

Section: Introductionmentioning

confidence: 99%

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IIB flux non-commutativity and the global structure of field theories

García-Etxebarria

Heidenreich

Regalado

2019

J. High Energ. Phys.

181

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We discuss the origin of the choice of global structure for six dimensional (2, 0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of N = 4 theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of N = 4 ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional (1, 0) theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects. arXiv:1908.08027v2 [hep-th] 9 Oct 20191 The separation into background and intrinsic data is sometimes arbitrary: if we restrict ourselves to fourdimensional Yang-Mills theories with constant coupling τ we could view τ as part of the data defining T . However, if we wish to allow for the possibility that τ varies across M then we must include it as part of the background data to be specified for each manifold. The second interpretation will be more natural from the point of view in this paper, and such configurations will play an interesting role below.2 In this paper we will take M6 to be closed, Spin and orientable, and furthermore we will assume that the cohomology groups of M6 are freely generated, so there is no torsion. 3 The free, or "abelian", (2, 0) theory can be obtained by replacing C 2 /Γ by a single-centered Taub-NUT space.5 The two groups are related by the short exact sequence 0 → W 4 → H 4 (M6 × S 3 /Zn; U (1)) → Tor(H 5 (M6 × S 3 /ZN ; Z)) → 0 , with W 4 the group of topologically trivial C4 Wilson lines on M6 × S 3 /Zn.

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Section: The Defect Group and The Linking Pairingmentioning

confidence: 99%

Section: Fractional Instanton Numbers and The Linking Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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IIB flux non-commutativity and the global structure of field theories

García-Etxebarria

Heidenreich

Regalado

2019

J. High Energ. Phys.

181

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“…As they do not admit a semi-classical limit, these theories are rather hard to study and are mainly known through their string theory constructions, which nevertheless yield enough information to construct their anomaly field theories. [30] Indeed, the local [17,31] and global [32] anomalies of 6d SCFT in the A series can be computed by considering anomaly cancellation on stacks of M5-branes in M-theory. The worldvolume of a stack of n M5branes is described in a certain decoupling limit by a A n 6d SCFT and a free tensor multiplet representing the center of mass.…”

Section: -Dimensional (20) Superconformal Field Theoriesmentioning

confidence: 99%

“…These geometric invariants can then be promoted to field theory functors. [30] The anomaly field theory is a product of several factors, associated to fermions, self-dual fields and Hopf-Wess-Zumino terms. [33] We will not make them explicit here, see [30].…”

Section: -Dimensional (20) Superconformal Field Theoriesmentioning

confidence: 99%

A Modern Point of View on Anomalies

Monnier

2019

Fortschritte der Physik

Self Cite

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We review the concept of anomaly field theory, namely the fact that the anomalies of a d‐dimensional field theory can be encoded in a d+1‐dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical facts about anomalies are recovered from the anomaly field theory, and review recent work on global anomaly cancellation in 6d supergravity where this concept was instrumental. We also sketch the status of global anomaly cancellation checks in string theory. This paper is based on a talk given at the Durham Symposium ‘Higher Structures in M‐theory’ in August 2018.

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Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

Eckhard

Kim

Schäfer‐Nameki

et al. 2020

J. High Energ. Phys.

101

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By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d (2, 0) theory on a three-manifold M 3 . This generalization is applicable to both the 3d N = 2 and N = 1 supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by M 3 . This is carried out in detail for M 3 a Seifert manifold, where we compute a refined version of the Witten index.In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on M 3 , which matches the Witten index computation that takes the higher-form symmetries into account.for which such 3d-3d duals have been discussed are the squashed three-sphere S 3 b [1, 2, 6], the superconformal index on S 2 × S 1 [3], and the twisted index on Σ g × S 1 [7]. The special case W 3 = T 3 was considered in [5,7] and computes the (regularized) Witten index [8] I = Tr(−1) F . 1 However, an important characteristic of the theories has so far been largely ignored: their higher-form symmetries [12]. Namely, the theory T [M 3 ] has a higher-form symmetry, which, as with other properties of T [M 3 ], is determined by the topology of M 3 . In fact, the theory T [M 3 ] is not fully specified by the manifold, M 3 , but requires additional topological data. This is related to the fact that the 6d N = (2, 0) theory itself is a relative QFT, i.e., it is only well-defined as the boundary of a 7d TQFT [13,14]. Equivalently, its observables depend on a choice of polarization, i.e., a choice of maximal isotropic subgroup of H 3 (M 3 , Z G ), where Z G is the center of the simply connected group, G, with Lie algebra g. Naturally, we expect that T [M 3 ] also depends on the polarization, as is the case for 4d theories [15,16]. In fact, we will see that this additional information translates into the residual 0-and 1-form symmetry of the 3d theory. We propose therefore a refined definition of the theories, which specifies this dataThis theory has a discrete 0-form (ordinary) symmetry group H. Its residual 1-form symmetry is given by the complementary subgroup, Υ H , 2 inside H 1 (M 3 , Z G ). We show that the choice of H can indeed be detected by the Witten index or, more generally, by the partition function on any W 3 with non-trivial homology. Thus, the different theories in (1.2) are indeed physically distinct.The main interest of this paper is to develop a sound definition of the theories T [M 3 , g, H]in (1.2) for M 3 a graph manifold [17], a class of three-manifolds we review in section 2.1. These manifolds, which also occur as the boundary of plumbed four-manifolds, are sometimes called plumbed three-manifolds, a special case of which are Seifert manifolds. Similar Lagrangians for the 3d theories associated to these manifolds were studied in [6,[18][19][20][21][22][23].In the following we point out new feat...

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The anomaly field theories of six-dimensional $(2,0)$ superconformal theories

Cited by 33 publications

References 37 publications

IIB flux non-commutativity and the global structure of field theories

IIB flux non-commutativity and the global structure of field theories

A Modern Point of View on Anomalies

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence

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