Modular Operads and Batalin-Vilkovisky Geometry
نویسندگان
چکیده
منابع مشابه
Framed Discs Operads and Batalin–vilkovisky Algebras
The framed n-discs operad f Dn is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by f Dn is equivalent to the n-fold loop space on an SO(n)-space. Examples of f D2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of f Dn , which produces higher Batalin–Vilko...
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We analyze the algebraic and geometric structures of deformations of Schwarz type topological field theories. Deformations of the Chern-Simons-BF theory and BF theories in n dimensions are analyzed. Two dimensionanl theory induces the Poisson structure and three dimensional theory induces the Courant algebroid structure on the target space as a sigma model. We generalize these structures to hig...
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2 Path Integrals 3 2.1 Gaussian Integrals and Beyond... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Gauge-fixing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Gauge-fixing: Faddeev—Popov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Gauge-fixing: BRST . . . . . . . . . . . . . . . . . . . . . . ...
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A Batalin-Vilkovisky formalism is most general framework to construct consistent quantum field theories. Its mathematical structure is called a BatalinVilkovisky structure. First we explain rather mathematical setting of a BatalinVilkovisky formalism. Next, we consider deformation theory of a BatalinVilkovisky structure. Especially, we consider deformation of topological sigma models in any dim...
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We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of the Batalin–Vilkovisky algebra. While such an operator of order 2 defines a Lie algebra structure on A, an operator of an order higher than 2 (Koszul–Akman definition) leads to the structure of a strongly homotopy Lie algebra (L∞–algebra) on A. This allows us to give a defin...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnm075