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DTSTART;TZID=America/New_York:20240912T100000
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DTSTAMP:20260622T031333
CREATED:20240907T170232Z
LAST-MODIFIED:20240917T140551Z
UID:10003412-1726135200-1726138800@cmsa.fas.harvard.edu
SUMMARY:Twisted Tools for (Untwisted) Quantum Field Theory
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Justin Kulp (Simons Center for Geometry and Physics) \nTitle: Twisted Tools for (Untwisted) Quantum Field Theory \nAbstract: One of the most important properties of QFTs is that they can be deformed by “turning on interactions.” Essentially every observable can be viewed as coupling the theory to some external system. Famously\, adding interactions (generically) breaks scale invariance\, leading to familiar ideas of EFTs and RG flows in the space of QFTs. An underappreciated fact is that one can actually consider flows generated by any transformation\, not just the usual scale transformations. \nIn my talk\, I will discuss a flow in the space of QFTs coming from (an analogue of) BRST symmetry. The beta-function for this “BRST-flow” controls deformations of the QFT and is highly mathematically constrained\, endowing the space of interactions with an L∞ algebra structure. The structure constants/brackets of the L∞ algebra are highly computable (requiring only a first course in QFT to compute) and contain familiar information such as anomalies and Operator Product Expansion coefficients. I will prove a non-renormalization theorem for holomorphic-topological QFTs with more than one topological direction\, which can be thought of as a generalization of a formality theorem of Kontsevich. Time permitting\, I will discuss how this formalism enables the systematic computation of minimal BPS operators in supersymmetric QFTs and describe the “holomorphic confinement” of N=1 SYM.  Based on arXiv:2403.13049.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematica-Physics-and-Algebraic-Geometry-09.12.2024.png
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