Omega vs. pi, and 6d anomaly cancellation

Davighi, Joe; Lohitsiri, Nakarin

doi:10.1007/jhep05(2021)267

Cited by 13 publications

(13 citation statements)

References 125 publications

(277 reference statements)

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“…(BG) ≤ p+q=5 E 2 p,q , we obtain the desired result. 11 This agrees with a more general (and more widely used) usage of the term cobordism to mean the (shifted) Anderson dual of the bordism group [8,38,52]. When G is finite and d = 4, as we consider here, the two coincide.…”

supporting

confidence: 81%

“…This cobordism classification of anomalies has been used in many contexts in recent years, with applications in both high energy physics (including string theory) and condensed matter physics. On the high energy side, applications include the elucidation of an order 16 anomaly in Spin×Z/4 Z/2 symmetry [12] and related anomalies [13], a new SU (2) anomaly for non-spin spacetimes [14], anomalies (and their absence) in the Standard Model (SM) and Beyond the SM [15][16][17][18][19][20], examples in 6d [11,21] and 8d [22,23], anomalies in duality groups [24,25], anomaly cancellation in heterotic string theory [26,27], and a newly discovered anomaly in Type IIB string theory [28].…”

Section: Introductionmentioning

confidence: 99%

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Anomalies of non-Abelian finite groups via cobordism

Davighi¹,

Gripaios²,

Lohitsiri³

2022

Preprint

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We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of 'anomaly interplay', which uses functoriality of cobordism and naturality of the η-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including S 3 , A 4 , Q 8 , and SL(2, F 3 ).In the case of finite abelian groups, it is well known that anomalies can be 'truncated' in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with A 4 symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2, F 3 ) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a Z/3 extension of SL(2, F 3 ).

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supporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Anomalies of non-Abelian finite groups via cobordism

Davighi¹,

Gripaios²,

Lohitsiri³

2022

Preprint

Self Cite

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show abstract

“…18 Mere the existence of a spin structure is not enough for locality; we need explicit spin structures on manifolds. 19 In the present situation of M-theory compactified on KB, there is a perfect candidate for such a 3-form Z 2 gauge field. We have discussed that the consistency requires that C = −C or 2C = 0 on M 9 up to gauge transformations.…”

Section: Jhep07(2022)125mentioning

confidence: 96%

“…Thus, a choice of v1 gives a spin structure. 19 One can find two manifolds N d and N d with a common boundary ∂N d = ∂N d such that spin structure exists on N d and N d , but not on N d ∪ N d . Thus, "the existence of a spin structure" (rather than explicit spin structure) is not a local concept.…”

Section: Jhep07(2022)125mentioning

confidence: 99%

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Global anomalies in 8d supergravity

Lee

Yonekura

2022

J. High Energ. Phys.

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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 $$ {\varOmega}_9^{\mathrm{spin}}(BG) $$ Ω 9 spin 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$$ \mathcal{N} $$ 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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Towards a complete classification of 6D supergravities

Hamada,

Loges

2024

J. High Energ. Phys.

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The constraints arising from anomaly cancellation are particular strong for chiral theories in six dimensions. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group. First, we generalize a previously known infinite class of anomaly-free theories which has 𝑇 ≫ 9 to essentially any semi-simple gauge group and infinitely many choices for hypermultiplets. The construction relies on having many decoupled sectors all selected from a list of four simple theories which we identify. Second, we use ideas from graph theory to rephrase the task of finding anomaly-free theories as constructing cliques in a certain multigraph. A branch-and-bound type algorithm is described which can be used to explicitly construct, in a 𝑇-independent way, anomaly-free theories with an arbitrary number of simple factors in the gauge group. We implement these ideas to generate an ensemble of $$ \mathcal{O} $$ O (107) irreducible cliques from which anomaly-free theories may be easily built, and as a special case obtain a complete list of 19,847 consistent theories for 𝑇 = 0, for which the maximal gauge group rank is 24. Modulo U(1), SU(2) and SU(3) simple factors and the new infinite families, we give a complete characterization of anomaly-free theories and show that the bound 𝑇 ≤ 273 is sharp.

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Omega vs. pi, and 6d anomaly cancellation

Cited by 13 publications

References 125 publications

Anomalies of non-Abelian finite groups via cobordism

Anomalies of non-Abelian finite groups via cobordism

Global anomalies in 8d supergravity

Towards a complete classification of 6D supergravities

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