Mixed global anomalies and boundary conformal field theories

Numasawa, Tokiro; Yamaguch, S.

doi:10.1007/jhep11(2018)202

Cited by 24 publications

(18 citation statements)

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“…It follows that the partition function Z L is invariant under the Γ 0 (2) congruence subgroup if the Z 2 is non-anomalous, and invariant under Γ 0 (4) if anomalous. The relation between the modular crossing equations and anomalies has been discussed extensively in [37][38][39][40][41].…”

Section: Modular Bootstrapmentioning

confidence: 99%

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Anomalies and bounds on charged operators

2019

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We study the implications of 't Hooft anomaly (i.e. obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is Z 2 . Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z 2 global symmetry are derived. The bootstrap bounds depend dramatically on the 't Hooft anomaly. In particular, there is a universal upper bound on the lightest Z 2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. In the non-anomalous case, we find that the lightest Z 2 odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a U (1) global symmetry, and comment that there is no bound on the lightest U (1) charged operator if the symmetry is non-anomalous.

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Section: Modular Bootstrapmentioning

confidence: 99%

“…where we have used L + = α L − . The computation of more general discrete group anomalies from the torus partition function is discussed in [37] (see also [38,40,41]).…”

Section: Computation Of the Anomalymentioning

confidence: 99%

Anomalies and bounds on charged operators

2019

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“…At θ " 0, the IR is trivially gapped, while at θ " π, the IR phase is gapless and is described by the SU p2q 1 WZW model which captures the mixed anomaly. One potential avenue to incorporate the information from 't Hooft anomalies into our index would be to interpret it as a torus partition function (possibly with symmetry lines inserted), whose modular transformation generally depends on the 't Hooft anomaly (see, for example, [41][42][43]).…”

Section: Discussionmentioning

confidence: 99%

An index for quantum integrability

2019

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The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question [1] of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index IpJq for each spin J, with the property that IpJq is a lower bound on the number of quantum conserved currents of spin J. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the CP N´1 model, the OpN q model, and the flag sigma model U pN q U p1q N . For the OpN q model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the CP N´1 model for N ą 2 are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model U pN q U p1q N for N ą 2 are all negative. Thus, it is unlikely that the flag sigma models are integrable.

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“…We first review the invariant boundary state condition in WZW models [4,24] for later discussions. To form the physical boundary states of Wess-Zumino-Witten models, we need a basis called Ishibashi states.…”

Section: Boundary States and Mixed Anomalymentioning

confidence: 99%

“…In [4], it has been proposed that one can use G-invariant boundary state condition in CFT 2 to justify whether there is a 't Hooft anomaly or not, namely the existence of a Ginvariant boundary state will imply that G is 't Hooft anomaly free. By this mean, [24] computed the anomaly free condition (conditions on the level k) for the center symmetry of Wess-Zumino-Witten models. Indeed this precisely agrees with the 1-form anomaly free conditions [3] of 3d Chern-Simons theories with general Lie groups, which justifies that the anomaly can flow from a bulk to a boundary.…”

Section: Introductionmentioning

confidence: 99%