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On globalized traces for the Poisson sigma model. (English) Zbl 1498.81106

Summary: A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin-Vilkovisky formalism. This global construction includes the concept of zero modes. Moreover, for the symplectic case of the Poisson Sigma Model with cotangent target, the globalized trace reduces to a symplectic construction which was presented by R. E. Grady et al. [Adv. Math. 317, 575–639 (2017; Zbl 1393.53090)] for 1-dimensional Chern-Simons theory (topological quantum mechanics). In addition, the connection between this formula and the Nest-Tsygan theorem and the Tamarkin-Tsygan theorem is explained.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
53D17 Poisson manifolds; Poisson groupoids and algebroids
18G65 Stable module categories

Citations:

Zbl 1393.53090
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References:

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