Abstract
We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the Batalin-Vilkovisky formalism is a differential graded Lie algebra.
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S. Axelrod and I.M. Singer, Chern-Simons perturbation theory, in International Conference on Differential Geometric Methods in Theoretical Physics, pp. 3–45 (1991) [hep-th/9110056] [INSPIRE].
G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in gauge theories, Phys. Rept. 338 (2000) 439 [hep-th/0002245] [INSPIRE].
G. Barnich and M. Grigoriev, A Poincaré lemma for sigma models of AKSZ type, J. Geom. Phys. 61 (2011) 663 [arXiv:0905.0547] [INSPIRE].
A.S. Cattaneo and G. Felder, On the AKSZ formulation of the Poisson sigma model, Lett. Math. Phys. 56 (2001) 163 [math/0102108] [INSPIRE].
A.S. Cattaneo, P. Mnev and N. Reshetikhin, Classical BV theories on manifolds with boundary, Commun. Math. Phys. 332 (2014) 535 [arXiv:1201.0290] [INSPIRE].
E. Getzler, A Darboux theorem for Hamiltonian operators in the formal calculus of variations, Duke Math. J. 111 (2002) 535 [math/0002164].
E. Getzler, Covariance in the Batalin-Vilkovisky formalism and the Maurer-Cartan equation for curved Lie algebras, Lett. Math. Phys. 109 (2019) 187 [arXiv:1801.04525] [INSPIRE].
W.M. Goldman and J.J. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Inst. Hautes Études Sci. Publ. Math. 67 (1988) 43.
J.E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin (1972), pp. xii+169 [DOI].
P.J. Olver, Applications of Lie groups to differential equations, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York (1986), pp. xxvi+497 [DOI].
V.O. Soloviev, Boundary values as Hamiltonian variables. 1. New Poisson brackets, J. Math. Phys. 34 (1993) 5747 [hep-th/9305133] [INSPIRE].
D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269.
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Getzler, E. Batalin-Vilkovisky formality for Chern-Simons theory. J. High Energ. Phys. 2021, 105 (2021). https://doi.org/10.1007/JHEP12(2021)105
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DOI: https://doi.org/10.1007/JHEP12(2021)105