Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24

Lam, Ching Hung; Shimakura, Hiroki
March 2012
Proceedings of the London Mathematical Society;Mar2012, Vol. 104 Issue 3, p540
Academic Journal
In 1993, Schellekens [‘Meromorphic c=24 conformal field theories’, Comm. Math. Phys. 153 (1993) 159–185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras (VOAs) using the theory of framed VOAs and to determine the Lie algebra structures of their weight 1 subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes RM(1, 4)3 and RM(1, 4)⊕ (d16+) of length 48. These VOAs correspond to the holomorphic simple current extensions of the lattice type VOAs and . We determine such extensions using a quadratic space structure on the set of all irreducible modules R(W) of W when or As our main results, we construct seven new holomorphic VOAs of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight 1 subspaces of holomorphic framed VOAs of central charge 24.


Related Articles

  • Rational vertex operator algebras and the effective central charge. Dong, Chongying; Mason, Geoffrey // IMRN: International Mathematics Research Notices;2004, Vol. 2004 Issue 56, p2989 

    We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c˜. We show that lattice vertex operator algebras may be characterized by the equalities c˜=l=c, and...

  • Pure Spinors in AdS and Lie Algebra Cohomology. Mikhailov, Andrei // Letters in Mathematical Physics;Oct2014, Vol. 104 Issue 10, p1201 

    We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS × S can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described...

  • Extension of unitary Virasoro vertex operator algebra by a simple module. Lam, Ching Hung; Lam, Ngau; Yamauchi, Hiroshi // IMRN: International Mathematics Research Notices;2003, Vol. 2003 Issue 11, p577 

    We study a certain extension of the Virasoro vertex operator algebra L(cm,0), where the central charge cm = 1 − 6/(m + 2)(m + 3), and m = 1,2,…. We show that the space L(cm,0)⊕ L(cm,hm) has a vertex operator algebra (or superalgebra) structure for some hm. When L(cm,0)⊕...

  • On the Constructions of Holomorphic Vertex Operator Algebras of Central Charge 24. Lam, Ching // Communications in Mathematical Physics;Jul2011, Vol. 305 Issue 1, p153 

    In this article, we construct explicitly several holomorphic vertex operator algebras of central charge 24 using Virasoro frames. The Lie algebras associated to their weight one subspaces are of the types $${A_{1,2} {A_{3,4}}^4, A_{1,2}D_{5,8}, {A_{1,1}}^3A_{7,4}}$$ , $${{A_{1,1}}^2 C_{3,2}...

  • A Characterization of the Moonshine Vertex Operator Algebra by Means of Virasoro Frames. Ching Hung Lam; Yamauchi, Hiroshi // IMRN: International Mathematics Research Notices;Jan2007, Vol. 2007, p1 

    In this article, we show that a framed vertex operator algebra (VOA) V satisfying the conditions: (i) V is holomorphic (i.e., V is the only irreducible V-module); (ii) V is of rank 24; and (iii) V1 = 0; is isomorphic to the moonshine VOA Vâ™® constructed by Frenkel-Lepowsky-Meurman [12].

  • The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras. Kawasetsu, Kazuya // Letters in Mathematical Physics;Feb2014, Vol. 104 Issue 2, p157 

    A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given. As an application, it is shown that the characters of some modules of an...

  • An explicit realization of logarithmic modules for the vertex operator algebra Wp,p′. Adamovic, Drazˇen; Milas, Antun // Journal of Mathematical Physics;Jul2012, Vol. 53 Issue 7, p073511 

    By extending the methods used in our earlier work, in this paper, we present an explicit realization of logarithmic Wp,p′-modules that have L(0) nilpotent rank three. This was achieved by combining the techniques developed in [D. Adamovic and A. Milas, 'Lattice construction of logarithmic...

  • TWISTED MODULES OF COLOURED LATTICE VERTEX OPERATOR SUPERALGEBRAS. XU, XIAOPING // Quarterly Journal of Mathematics;1996, Vol. 47 Issue 2, p233 

    The article presents a study which describes the classical solutions and twisted modules of coloured lattice in vertex operator superalgebras. It explores the representations of affine algebras of twisted modules, such as the Monster moonshine module and the associated automorphism induced by...

  • Quantum integrable systems and representations of Lie algebras. Etingof, Pavel I. // Journal of Mathematical Physics;Jun95, Vol. 36 Issue 6, p2636 

    Discusses the construction of the quantum integrals for the Hamiltonian in the trigonometric and elliptic cases using representation theory of Lie algebras. Eigenfunctions of the quantum integrals; Validation of the integrability theorem; Formulation of vertex operators, correlation functions...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics