Advertisement

Permutation Orbifolds of Rank Three Fermionic Vertex Superalgebras

  • Antun MilasEmail author
  • Michael Penn
  • Josh Wauchope
Chapter
First Online:
Part of the Springer INdAM Series book series (SINDAMS, volume 37)

Abstract

We describe the structure of the permutation orbifold of the rank three free fermion vertex superalgebra (of central charge \(\frac{3}{2}\)) and of the rank three symplectic fermion vertex superalgebra (of central charge \(-6\)).

Keywords

Fermions Vertex algebras \(\mathcal {W}\)-algebras 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

A.M. would like to thank T. Creutzig for discussion regarding Sect. 3.2. He would also like to thank D. Adamovic and P. Papi for invitation and hospitality during the conference Affine, vertex and W-algebras, INdAM, Rome, December 11–15, 2017. We also thank the referee for useful comments.

References

  1. 1.
    Adamovic, D., Milas, A.: On the triplet vertex algebra \(W(p)\). Adv. Math. 217, 2664–2699 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Adamovic, D., Lin, X., Milas, A.: ADE subalgebras of the triplet vertex algebra W(p): A-series. Commun. Contemp. Math. 15, 1350028 (2013) 30 ppMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Adamovic, D., Lin, X., Milas, A.: ADE subalgebras of the triplet vertex algebra; D-series. Int. J. Math. 25(1), 1450001 (2014) 34 ppMathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Adamovic, D., Perse, O.: On coset vertex algebras with central charge. Math. Commun. 15(1), 143–157 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Abe, T.: \(C_2\)-cofiniteness of 2-cyclic permutation orbifold models. Commun. Math. Phys. 317(2), 425–445 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bouwknegt, P., Schoutens, K.: W-symmetry in conformal field theory. Phys. Rep. 223(4), 183–276 (1993)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Creutzig, T., Linshaw, A.: Orbifolds of symplectic fermion algebras. Trans. Am. Math. Soc. 369, 467–494 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Chandrasekhar, O., Penn, M., Shao, H.: \(\mathbb{Z}_2\) orbifolds of free fermion algebras. Commun. Algebr. 46, 4201–4222 (2018)zbMATHCrossRefGoogle Scholar
  9. 9.
    Dong, C., Jiang, C.: Representations of the vertex operator algebra \(V_{L2}^{A4}\). J. Algebr. 377, 76–96 (2013)CrossRefGoogle Scholar
  10. 10.
    Dong, C., Mason, G.: Rational vertex operator algebras and the effective central charge. IMRN 56, 2989–3008 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dong, C., Xu, F., Yu, N.: The 3-permutation orbifold of a lattice vertex operator algebra. J. Pure Appl. Algebr. (2017)Google Scholar
  12. 12.
    Genra, N.: Screening operators for \(\cal{W}\)-algebras. Selecta Math. 23(3), 2157–2202 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Kac, V., Roan, S.S., Wakimoto, M.: Quantum reduction for affine superalgebras. Commun. Math. Phys. 241(2), 307–342 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Kac, V.G., Raina, A.K.: Bombay Lectures on Highest Weight Representations. World scientific, Singapore (1987)zbMATHGoogle Scholar
  15. 15.
    Linshaw, A.: A Hilbert theorem for vertex algebras. Transform. Groups 15(2), 427–448 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Linshaw, A.: The structure of the Kac–Wang–Yan algebra. Commun. Math. Phys. 345(2), 545–585 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Linshaw, A.: Invariant subalgebras of affine vertex algebras. Adv. Math. 234, 61–84 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Lin, X.: ADE subalgebras of the triplet vertex algebra W(p): \(E_6, E_7\). Int. Math. Res. Not. 2015(15), 6752–6792 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Milas, A., Penn, M., Shao, H.: Permutation orbfolds of the Heisenberg vertex algebra, \(\cal{H}(3)\). J. Math. Phys. (To appear). arXiv.1804.01036
  20. 20.
    Milas, A., Penn, M. in preparationGoogle Scholar
  21. 21.
    Smith, L.: Polynomial Invariants of Finite Groups. Research Notes in Mathematics, vol. 6. A K Peters/CRC Press, Boca Raton (1995)zbMATHCrossRefGoogle Scholar
  22. 22.
    Theilman, K.: Mathematica Package OPE (1991)Google Scholar
  23. 23.
    Watts, G.M.T.: \(WB\) algebra representation theory. Nucl. Phys. B 339, 177 (1990)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Weyl, H.: The Classical Groups: Their Invariants and Representations. Princeton University Press, Princeton (1946)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSUNY-AlbanyAlbanyUSA
  2. 2.Randolph CollegeLynchburgUSA

Personalised recommendations

Cite chapter

Buy options