Built on

C. Beem, C. Meneghelli, and L. Rastelli, “Free Field Realizations from the Higgs Branch,” arXiv:1903.07624 [hep-th]
Original
1903
Earlier work this paper cites.
A. D. Shapere and Y. Tachikawa, “Central charges of N=2 superconformal field theories in four dimensions,” JHEP
Original
1957
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R. W. Carter, “Conjugacy classes in the weyl group,” Compositio Mathematica
1972
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R. P. Stanley, “Invariants of finite groups and their applications to combinatorics,” Bull. Amer. Math. Soc. (N.S.)
1979
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PhD thesis, Leuven U., 1994
K. Thielemans, An Algorithmic approach to operator product expansions, W algebras and W strings · 1994
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F. Cachazo, M. R. Douglas, N. Seiberg, and E. Witten, “Chiral rings and anomalies in supersymmetric gauge theory,” JHEP
2002
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M. Geck and G. Malle, “Reflection Groups. A Contribution to the Handbook of Algebra,” arXiv Mathematics e-prints
2003
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F. A. Dolan and H. Osborn, “On short and semi-short representations for four-dimensional superconformal symmetry,” Annals Phys
2003
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V. G. Kac and M. Wakimoto, “Quantum reduction and representation theory of superconformal algebras,” Advances in Mathematics
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J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 dimensional super conformal theories,” Commun. Math. Phys
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I. V. Dolgachev, “Reflection groups in algebraic geometry,” Bull. Amer. Math. Soc. (N.S.)
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Cambridge University Press, 2009
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T. Arakawa, “A remark on the c 2-cofiniteness condition on vertex algebras,” Mathematische Zeitschrift
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A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, “Gauge Theories and Macdonald Polynomials,” Commun. Math. Phys
Original
2013
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2018

VOAs labelled by complex reflection groups and 4d SCFTs

Bonetti, Federico, Meneghelli, Carlo, Rastelli, Leonardo

Understand

We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups.

They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group $\mathcal{\mathsf{G}}$.
If $\mathcal{\mathsf{G}}$ is a Coxeter group, the $\mathcal{N}=2$ super Virasoro algebra enhances to the (small) $\mathcal{N}=4$ superconformal algebra.
With the exception of $\mathcal{\mathsf{G}} = \mathbb{Z}_2$, which corresponds to just the $\mathcal{N}=4$ algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge.

Built on

C. Beem, C. Meneghelli, and L. Rastelli, “Free Field Realizations from the Higgs Branch,” arXiv:1903.07624 [hep-th]
Original
1903
Earlier work this paper cites.
A. D. Shapere and Y. Tachikawa, “Central charges of N=2 superconformal field theories in four dimensions,” JHEP
Original
1957
Earlier work this paper cites.
R. W. Carter, “Conjugacy classes in the weyl group,” Compositio Mathematica
1972
Earlier work this paper cites.
R. P. Stanley, “Invariants of finite groups and their applications to combinatorics,” Bull. Amer. Math. Soc. (N.S.)
1979
Earlier work this paper cites.
PhD thesis, Leuven U., 1994
K. Thielemans, An Algorithmic approach to operator product expansions, W algebras and W strings · 1994
Earlier work this paper cites.
F. Cachazo, M. R. Douglas, N. Seiberg, and E. Witten, “Chiral rings and anomalies in supersymmetric gauge theory,” JHEP
2002
Earlier work this paper cites.
M. Geck and G. Malle, “Reflection Groups. A Contribution to the Handbook of Algebra,” arXiv Mathematics e-prints
2003
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “On short and semi-short representations for four-dimensional superconformal symmetry,” Annals Phys
2003
Earlier work this paper cites.
V. G. Kac and M. Wakimoto, “Quantum reduction and representation theory of superconformal algebras,” Advances in Mathematics
2004
Earlier work this paper cites.
J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 dimensional super conformal theories,” Commun. Math. Phys
2007
Earlier work this paper cites.
I. V. Dolgachev, “Reflection groups in algebraic geometry,” Bull. Amer. Math. Soc. (N.S.)
2008
Earlier work this paper cites.
Cambridge University Press, 2009
G. I. Lehrer and D. E. Taylor, Unitary Reflection Groups · 2009
Earlier work this paper cites.
T. Arakawa, “A remark on the c 2-cofiniteness condition on vertex algebras,” Mathematische Zeitschrift
Original
2012
Earlier work this paper cites.
A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, “Gauge Theories and Macdonald Polynomials,” Commun. Math. Phys
Original
2013
Earlier work this paper cites.