Communications in Mathematical Physics

, Volume 303, Issue 2, pp 331–359 | Cite as

Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory

  • Anton M. ZeitlinEmail author


We define a quasiclassical limit of the Lian-Zuckerman homotopy BV algebra (quasiclassical LZ algebra) on the subcomplex, corresponding to “light modes”, i.e. the elements of zero conformal weight, of the semi-infinite (BRST) cohomology complex of the Virasoro algebra associated with vertex operator algebra (VOA) with a formal parameter. We also construct a certain deformation of the BRST differential parametrized by a constant two-component tensor, such that it leads to the deformation of the A -subalgebra of the quasiclassical LZ algebra. Altogether this gives a functor the category of VOA with a formal parameter to the category of A -algebras. The associated generalized Maurer-Cartan equation gives the analogue of the Yang-Mills equation for a wide class of VOAs. Applying this construction to an example of VOA generated by β - γ systems, we find a remarkable relation between the Courant algebroid and the homotopy algebra of the Yang-Mills theory.


Gauge Theory Conformal Weight Vertex Algebra Ghost Number Double Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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