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Background Fields, Quantum Tunneling, and Derived Stacks

Student-Run Algebraic Geometry Seminar

Speaker: John Murray
Location: 2112 MSB
Start time: Wed, Nov 15 2017, 2:00PM

Building on formalisms developed by Costello and Gwilliam, we construct families of quantum field theories parameterized by classical background fields. In particular, our construction allows for the quantization of classical field theories in instanton backgrounds. We accomplish this by translating techniques from the background field method into the language of higher categories and derived geometry. Lastly, we explain how the nonperturbative effect of quantum tunneling is realized via the quantization of higher simplices in the space of background fields. Throughout the talk we will focus on developing these ideas for Chern-Simons theory as a concrete example.