Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
conformal field theory; conformal blocks; recursion formulas; vertex algebras
conformal field theory; conformal blocks; recursion formulas; vertex algebras
Summary:
A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find $n$-point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg and free fermionic vertex operator algebras are supplied.
References:
[1] Belavin, A., Polyakov, A., Zamolodchikov, A.: Infinite conformal symmetries in two-dimensional quantum field theory. Nuclear. Phys. B 241 (1984), 333–380. DOI 10.1016/0550-3213(84)90052-X | MR 0757857
[2] Ben-Zvi, D., Frenkel, E.: Vertex algebras and algebraic curves. Mathematical Surveys and Monographs, vol. 88, American Mathematical Society, Providence, RI, 2004, Second ed. MR 2082709 | Zbl 1106.17035
[3] Borcherds, R.E.: Vertex algebras, Kac-Moody algebras and the Monster. Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 3068–3071. DOI 10.1073/pnas.83.10.3068 | MR 0843307 | Zbl 0613.17012
[4] Dong, C., Lepowsky, J.: Generalized Vertex Algebras and Relative Vertex Operators. Progr. Math., vol. 112, Birkhäuser (Boston, MA), 1993. MR 1233387 | Zbl 0803.17009
[5] Frenkel, I., Huang, Y., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Mem. Amer. Math. Soc. 104 (494) (1993), viii+64 pp. MR 1142494 | Zbl 0789.17022
[6] Frenkel, I. B., Lepowsky, J., Meurman, A.: Vertex Operator Algebras and the Monster. Pure Appl. Math., vol. 134, Academic Press, Boston, 1988. MR 0996026 | Zbl 0674.17001
[7] Friedan, D., Shenker, S.: The analytic geometry of two dimensional conformal field theory. Nuclear Phys. B 281 (1987), 509–545. MR 0869564
[8] Gilroy, T.: Genus Two Zhu Theory for Vertex Operator Algebras. Ph.D. thesis, NUI Galway, 2013, 1–89.
[9] Gunning, R.C.: Lectures on Riemann Surfaces. Princeton Univ. Press, Princeton, 1966. MR 0207977 | Zbl 0175.36801
[10] Hurley, D., Tuite, M.P.: Virasoro correlation functions for vertex operator algebras. Internat. J. Math. 23 (10) (2012), 17 pp., 1250106. DOI 10.1142/S0129167X12501066 | MR 2999051 | Zbl 1335.17016
[11] Kac, V.: Vertex Operator Algebras for Beginners. University Lecture Series, vol. 10, AMS, Providence, 1998.
[12] Kawamoto, N., Namikawa, Y., Tsuchiya, A., Yamada, Y.: Geometric realization of conformal field theory on Riemann surfaces. Comm. Math. Phys. 116 (1988), 247–308. DOI 10.1007/BF01225258 | MR 0939049 | Zbl 0648.35080
[13] Mason, G., Tuite, M.P.: Torus chiral $n$-point functions for free boson and lattice vertex operator algebras. Comm. Math. Phys. 235 (1) (2003), 47–68. DOI 10.1007/s00220-002-0772-6 | MR 1969720 | Zbl 1020.17020
[14] Mason, G., Tuite, M.P.: Free bosonic vertex operator algebras on genus two Riemann surfaces I. Comm. Math. Phys. 300 (2010), 673–713. DOI 10.1007/s00220-010-1126-4 | MR 2736959 | Zbl 1226.17024
[15] Mason, G., Tuite, M.P.: Vertex operators and modular forms. A window into zeta and modular physics. Math. Sci. Res. Inst. Publ., vol. 57, Cambridge Univ. Press, Cambridge, 2010, pp. 183–278. MR 2648364
[16] Mason, G., Tuite, M.P.: Free bosonic vertex operator algebras on genus two Riemann surfaces II. Contributions in Mathematical and Computational Sciences 8, Springer-Verlag, Berlin-Heidelberg, 2014. MR 2736959 | Zbl 1329.17027
[17] Mason, G., Tuite, M.P., Zuevsky, A.: Torus $n$-point functions for $\mathbb{R}$-graded vertex operator superalgebras and continuous fermion orbifolds. Comm. Math. Phys. 283 (2008), 305–342. DOI 10.1007/s00220-008-0510-9 | MR 2430636
[18] Matsuo, A., Nagatomo, K.: Axioms for a vertex algebra and the locality of quantum fields. MSJ Memoirs 4 (1999), x+110 pp. MR 1715197 | Zbl 0928.17025
[19] Serre, J.-P.: A course in Arithmetic. Springer-Verlag, Berlin, 1978. MR 0344216 | Zbl 0432.10001
[20] Tsuchiya, A., Ueno, K., Yamada, Y.: Conformal field theory on universal family of stable curves with gauge symmetrie. Adv. Stud. Pure Math. 19 (1989), 459–566. MR 1048605
[21] Tuite, M.P., Zuevsky, A.: Genus two partition and correlation functions for fermionic vertex operator superalgebras II. arXiv:1308.2441v1, submitted. MR 2824477
[22] Tuite, M.P., Zuevsky, A.: Genus two partition and correlation functions for fermionic vertex operator superalgebras I. Comm. Math. Phys. 306 (2011), 419–447. DOI 10.1007/s00220-011-1258-1 | MR 2824477 | Zbl 1254.17024
[23] Tuite, M.P., Zuevsky, A.: The Szegö kernel on a sewn Riemann surface. Comm. Math. Phys. 306 (2011), 617–645. DOI 10.1007/s00220-011-1310-1 | MR 2825503 | Zbl 1238.30029
[24] Tuite, M.P., Zuevsky, A.: A generalized vertex operator algebra for Heisenberg intertwiners. J. Pure Appl. Algebra 216 (2012), 1442–1453. DOI 10.1016/j.jpaa.2011.10.025 | MR 2890514 | Zbl 1287.17050
[25] Ueno, K.: Introduction to conformal field theory with gauge symmetries. Geometry and Physics - Proceedings of the Conference at Aarhus Univeristy, Aarhus, Denmark, New York, Marcel Dekker, 1997. MR 1423195 | Zbl 0873.32022
[26] Zhu, Y.: Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9 (1996), 237–302. DOI 10.1090/S0894-0347-96-00182-8 | MR 1317233 | Zbl 0854.17034
Search
Partner of
