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arXiv · 1912.11202

Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing

Santosh Kandel·Pavel Mnev·Konstantin Wernli
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Abstract

We study the perturbative quantization of 2-dimensional massive scalar field theory with polynomial (or power series) potential on manifolds with boundary. We prove that it fits into the functorial quantum field theory framework of Atiyah-Segal. In particular, we prove that the perturbative partition function defined in terms of integrals over configuration spaces of points on the surface satisfies an Atiyah-Segal type gluing formula. Tadpoles (short loops) behave nontrivially under gluing and play a crucial role in the result.

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Santosh Kandel, Pavel Mnev, Konstantin Wernli. 2019-12-24. Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing. https://doi.org/10.4310/atmp.2021.v25.n7.a5

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