Anomalies of fermionic CFTs via cobordism and bootstrap

Grigoletto, Andrea

doi:10.48550/arxiv.2112.01485

Cited by 2 publications

(4 citation statements)

References 52 publications

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“…JHEP09(2022)147 where x, y are degree 1 generators of H • (BQ 8 ; Z/2) and Arf is the Arf invariant of the spin structure. This phenomenon that free fermions do not account for every possible anomaly given by the cobordism group has also been observed in 2d when the symmetry group is the dihedral group D 8 [40].…”

Section: G = Qmentioning

confidence: 59%

“…The exponentiated η-invariant is a natural transformation from the functor RU (•) to the functor 6 Spin (B•) [39,40]. This means that, given a homomorphism f : G → K between finite groups, there are pullbacks induced on both these functors,…”

Section: Jhep09(2022)147mentioning

confidence: 99%

“…This version of anomaly interplay, in which both groups involved are finite, has been applied to the study of anomalies in two-dimensions in refs. [39,40]. 13 One particular trick we will frequently employ is to pullback whole short exact sequences that relate a non-abelian group G to abelian finite groups.…”

Section: Jhep09(2022)147mentioning

confidence: 99%

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Anomalies of non-Abelian finite groups via cobordism

Davighi

Gripaios

Lohitsiri

2022

J. High Energ. Phys.

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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 S3, A4, Q8, and SL(2, 𝔽3).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 A4 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, 𝔽3) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a ℤ/3 extension of SL(2, 𝔽3).

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Section: G = Qmentioning

confidence: 59%

Section: Jhep09(2022)147mentioning

confidence: 99%

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Anomalies of non-Abelian finite groups via cobordism

Davighi

Gripaios

Lohitsiri

2022

J. High Energ. Phys.

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“…This approach, termed modular bootstrap, has also been generalized to bosonic, (1+1)d CFTs with anomalous and non-anomalous Z N global symmetries by imposing modular covariance of the torus partition function twisted by symmetry defects 24,25 , as we mentioned. Additional progress in a similar vein has been made for fermionic CFTs with non-anomalous and anomalous global symmetries [45][46][47] , but in this work we will focus on bosonic theories.…”

Section: B Background Methods and Motivationmentioning

confidence: 93%

Bootstrapping Lieb-Schultz-Mattis anomalies

Lanzetta¹,

Fidkowski²

2022

Preprint

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We incorporate the microscopic assumptions that lead to a certain generalization of the Lieb-Schultz-Mattis (LSM) theorem for one-dimensional spin chains into the conformal bootstrap. Our approach accounts for the "LSM anomaly" possessed by these spin chains through a combination of modular bootstrap and correlator bootstrap of symmetry defect operators. We thus obtain universal bounds on the local operator content of (1+1)d conformal field theories (CFTs) that could describe translationally invariant lattice Hamiltonians with a ZN × ZN symmetry realized projectively at each site. We present bounds on local operators both with and without refinement by their global symmetry representations. Interestingly, we can obtain non-trivial bounds on charged operators when N is odd, which turns out to be impossible with modular bootstrap alone. Our bounds exhibit distinctive kinks, some of which are approximately saturated by known theories and others that are unexplained. We discuss additional scenarios with the properties necessary for our bounds to apply, including certain multicritical points between (1+1)d symmetry protected topological phases, where we argue that the anomaly studied in our bootstrap calculations should emerge.

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Anomalies of fermionic CFTs via cobordism and bootstrap

Cited by 2 publications

References 52 publications

Anomalies of non-Abelian finite groups via cobordism

Anomalies of non-Abelian finite groups via cobordism

Bootstrapping Lieb-Schultz-Mattis anomalies

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