Abstract
In this paper we study the existence of Virasoro structures in the twisted vertex algebra describing the particle correspondence of type C. We show that this twisted vertex algebra has at least two distinct Virasoro structures: one with central charge 1, and a second with central charge − 1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anguelova, I.I.: Boson-fermion correspondence of type B and twisted vertex algebras. In: Proceedings of the 9-th Workshop “Lie Theory and Its Applications in Physics” (LT-9), Varna, Bulgaria. Springer Proceedings in Mathematics and Statistics. Springer, Tokyo/Heidelberg (2013)
Anguelova, I.I.: Twisted vertex algebras, bicharacter construction and boson-fermion correspondences. J. Math. Phys. 54, 38pp, 121702 (2013)
Anguelova, I.I.: Boson-fermion correspondence of type D-A and multi-local Virasoro representations on the Fock space \(F \otimes \frac{1} {2}\). to appear in J. Math. Phys., (2014). arXiv:1406.5158 [math-ph]
Anguelova, I.I., Cox, B., Jurisich, E.: N-point locality for vertex operators: normal ordered products, operator product expansions, twisted vertex algebras. J. Pure Appl. Algebra 218(12), 2165–2203 (2014)
Bogoliubov, N.N., Shirkov, D.V.: Quantum Fields. Benjamin/Cummings Publishing Co. Inc. Advanced Book Program, Reading (1983)
Cox, B., Guo, X., Lu, R., Zhao, K.: N-point virasoro algebras and their modules of densities. arXiv:1308.6815 (2013)
Date, E., Jimbo, M., Kashiwara, M., Miwa, T.: Transformation groups for soliton equations. VI. KP hierarchies of orthogonal and symplectic type. J. Phys. Soc. Jpn 50(11), 3813–3818 (1981)
Date, E., Kashiwara, M., Miwa, T.: Transformation groups for soliton equations. II. Vertex operators and τ functions. Proc. Jpn Acad. Ser. A Math. Sci. 57(8), 387–392 (1981)
Frenkel, I.B.: Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. J. Funct. Anal. 44(3), 259–327 (1981)
Frenkel, E., Ben-Zvi, D.: Vertex Algebras and Algebraic Curves. Mathematical Surveys and Monographs, vol. 88, 2nd edn. American Mathematical Society, Providence (2004)
Frenkel, I., Lepowsky, J., Meurman, A.: Vertex Operator Algebras and the Monster. Pure and Applied Mathematics, vol. 134. Academic Press Inc., Boston (1988)
Frenkel, I., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Mem. Am. Math. Soc. 104(494), viii+64 (1993)
Huang, K.: Quantum Field Theory: From Operators to Path Integrals. Wiley, New York (1998)
Kac, V.G., Raina, A.K.: Bombay Lectures on Highest Weight Representations of Infinite-Dimensional Lie Algebras. Advanced Series in Mathematical Physics, vol. 2. World Scientific Publishing Co. Inc., Teaneck (1987)
Kac, V.: Vertex Algebras for Beginners. University Lecture Series, vol. 10, 2nd edn. American Mathematical Society, Providence (1998)
Krichever, I.M., Novikov, S.P.: Algebras of Virasoro type, Riemann surfaces and strings in Minkowski space. Funktsional. Anal. i Prilozhen. 21(4):47–61, 96, (1987).
Krichever, I.M., Novikov, S.P.: Algebras of Virasoro type, the energy-momentum tensor, and operator expansions on Riemann surfaces. Funktsional. Anal. i Prilozhen. 23(1), 24–40 (1989)
Lepowsky, J., Li, H.: Introduction to Vertex Operator Algebras and Their Representations. Progress in Mathematics, vol. 227. Birkhäuser, Boston (2004)
Schlichenmaier, M.: Differential operator algebras on compact Riemann surfaces. In: Generalized Symmetries in Physics (Clausthal, 1993), pp. 425–434. World Scientific Publishing, River Edge (1994)
van de Leur, J.W., Orlov, A.Y., Shiota, T.: CKP hierarchy, bosonic tau function and bosonization formulae. SIGMA 8, 28pp, 036 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this paper
Cite this paper
Anguelova, I.I. (2014). Virasoro Structures in the Twisted Vertex Algebra of the Particle Correspondence of Type C. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_33
Download citation
DOI: https://doi.org/10.1007/978-4-431-55285-7_33
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55284-0
Online ISBN: 978-4-431-55285-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)