Poisson sigma model with branes and hyperelliptic Riemann surfaces

Ferrario, Andrea

doi:10.1063/1.2982234

Cited by 6 publications

(7 citation statements)

References 21 publications

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“…We finally observe that all previous formulae are special cases of the main result in [9], where general (super)propagators for the Poisson σ-model in the presence of n branes, n ≥ 1, are explicitly produced.…”

Section: 32mentioning

confidence: 71%

Bimodules and branes in deformation quantization

Calaque¹,

Felder²,

Ferrario³

et al. 2010

Compositio Math.

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Section: 32mentioning

confidence: 71%

Bimodules and branes in deformation quantization

Calaque¹,

Felder²,

Ferrario³

et al. 2010

Compositio Math.

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“…Even though not justified in terms of the BV formalism, this choice of propagator was done before in [2] for Chern-Simons theory out of purely topological reasons, and later extended to BF theories in [7]. A propagator with these properties also appears in [13] for the Poisson sigma model on the interior of a polygon.…”

Section: Bv Formalism and Zero Modesmentioning

confidence: 99%

“…The differential forms are obtained from the propagator ω, see (14), and the form φ, see (13). Let Γ ∈ G (k1,...,kn),m .…”

Section: Weightsmentioning

confidence: 99%

Effective Batalin–Vilkovisky Theories, Equivariant Configuration Spaces and Cyclic Chains

Cattaneo

Felder

2010

Progress in Mathematics

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Summary. Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L∞-quasi-isomorphic to its cohomology. The construction of the L∞-map is given in terms of integrals of differential forms on configuration spaces of points in the upper half-plane. Here we consider configuration spaces of points in the disk and work equivariantly with respect to the rotation group. This leads to considering the differential graded Lie algebra of multivector fields endowed with a divergence operator. In the case of R d with standard volume form, we obtain an L∞-morphism of modules over this differential graded Lie algebra from cyclic chains of the algebra of functions to multivector fields. As a first application we give a construction of traces on algebras of functions with star-products associated with unimodular Poisson structures. The construction is based on the Batalin-Vilkovisky quantization of the Poisson sigma model on the disk and in particular on the treatment of its zero modes.

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“…We have an explicit propagator for the PSM, i.e. using the superfields of it, on a disk with alternating boundary conditions, which was computed in [14], in [26] and, in full generality, in [31]. C.1.…”

Section: Appendix C On the Propagatormentioning

confidence: 99%

On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism

Cattaneo

Moshayedi

Wernli

2020

Commun. Math. Phys.

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We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum GBFV operator on the total space of states is a differential, i.e. squares to zero, which is necessary for a well-defined BV cohomology.

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Poisson sigma model with branes and hyperelliptic Riemann surfaces

Cited by 6 publications

References 21 publications

Bimodules and branes in deformation quantization

Bimodules and branes in deformation quantization

Effective Batalin–Vilkovisky Theories, Equivariant Configuration Spaces and Cyclic Chains

On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism

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