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Free bosonic vertex operator algebras on genus two Riemann surfaces. II. (English) Zbl 1329.17027
Kohnen, Winfried (ed.) et al., Conformal field theory, automorphic forms and related topics. CFT 2011, Heidelberg, Germany, September 19–23, 2011. Berlin: Springer (ISBN 978-3-662-43830-5/hbk; 978-3-662-43831-2/ebook). Contributions in Mathematical and Computational Sciences 8, 183-225 (2014).
In this article Mason and Tuite continue their previous work [Commun. Math. Phys. 300, No. 3, 673–713 (2010; Zbl 1226.17024)] on vertex operator algebras on a compact Riemann surface in the context of $$n$$-point correlation functions. They study the generating function for Heisenberg $$n$$-point functions of genus two. It is shown that the Virasoro 1-point function satisfies a Ward identity. Formulas for the partition function in the context of free bosonic theories are obtained. Finally, they compare the results within two different formalisms. One is the present formalism, another is the so-called $$\epsilon$$-formalism discussed previously. The reader will be surprised by the fact that all $$n$$-point functions in these two formalisms are incompatible. There is a wealth of related ideas in the literature, in particular in the context of bosonic strings and conformal field theories. Relevant articles can be found in the large amount of References at the end.
For the entire collection see [Zbl 1297.00041].

##### MSC:
 17B69 Vertex operators; vertex operator algebras and related structures 17B70 Graded Lie (super)algebras 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations
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