Rectangular W-algebras of types so(M) and sp(2M) and dual coset CFTs

Creutzig, Thomas; Hikida, Yasuaki; Uetoko, Takahiro

doi:10.1007/jhep10(2019)023

“…• Orthogonal group So far we have considered the special unitary group in the coset model. We can apply the present results for the unitary group to the orthogonal group [39] where they decompose the SU(M ) generators into M (M −1)…”

Section: Discussionmentioning

confidence: 95%

The Grassmannian-like coset model and the higher spin currents

Ahn

¹

2021

J. High Energ. Phys.

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In the Grassmannian-like coset model, $$ \frac{\mathrm{SU}{\left(N+M\right)}_k}{\mathrm{SU}{(N)}_k\times \mathrm{U}{(1)}_{kNM\left(N+M\right)}} $$ SU N + M k SU N k × U 1 kNM N + M , Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of MM matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.

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“…As mentioned at the beginning of the introduction, W-algebras play important roles in several places of theoretical physics. In fact, one of our prime purposes to initiate this project is to understand the properties of conformal field theories dual to extended higher spin gravities as analyzed in [60,61,62]. In particular, it would be important to incorporate extended supersymmetry to see the relation between superstrings and higher spin gravities, see [63,64] for N = 4 supersymmtry and [65,66] for N = 3 supersymmetry.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Correlator correspondences for Gaiotto-Rapčák dualities and first order formulation of coset models

Creutzig¹,

Hikida²

2021

Preprint

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We derive correspondences of correlation functions among dual conformal field theories in two dimensions by developing a "first order formulation" of coset models. We examine several examples, and the most fundamental one may be a conjectural equivalence between a coset (SL(n) k ⊗ SL(n) −1 )/SL(n) k+1 and sl(n) Toda field theory with generic level k. Among others, we also complete the derivation of higher rank FZZ-duality involving a coset SL(n + 1) k /(SL(n) k ⊗ U (1)), which could be done only for n = 2, 3 in our previous paper. One obstacle in the previous work was our poor understanding of a first order formulation of coset models. In this paper, we establish such a formulation using the BRST formalism. With our better understanding, we successfully derive correlator correspondences of dual models including the examples mentioned above. The dualities may be regarded as conformal field theory realizations of some of the Gaiotto-Rapčák dualities of corner vertex operator algebras.

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“…• Orthogonal group So far we have considered the special unitary group in the coset model. We can apply the present results for the unitary group to the orthogonal group [38] where they decompose the SU(M) generators into M (M −1) 2 antisymmetric matrices and (M 2 − 1) − M (M −1) 2 traceless symmetric matrices. For the former, we do have spin-1 current and for the latter, we can associate with the spin-2 current.…”

Section: • Three Point Functionsmentioning

confidence: 93%

The Grassmannian-like Coset Model and the Higher Spin Currents

Ahn

2020

Preprint

0

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In the Grassmannian-like coset model, SU (N +M ) k SU (N ) k ×U (1) kNM (N+M ) , Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of M × M matrix generalization of AdS 3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.On the occasion of my sixtieth birthday 7.1 The OPE J a (z) W (3)

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Rectangular W-algebras of types so(M) and sp(2M) and dual coset CFTs

Cited by 11 publications

References 47 publications

The Grassmannian-like coset model and the higher spin currents

The Grassmannian-like coset model and the higher spin currents

Correlator correspondences for Gaiotto-Rapčák dualities and first order formulation of coset models

The Grassmannian-like Coset Model and the Higher Spin Currents

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