# Twisted Tools for (Untwisted) Quantum Field Theory

#### Twisted Tools for (Untwisted) Quantum Field Theory

- Event time: 2:00pm until 3:00pm
- Event date: 19th June 2024
- Speaker: Dr Justin Kulp (Stony Brook)
- Location: Room 4325B, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

One of the most important properties of quantum field theories is that they can be deformed by "turning on interactions." Indeed, essentially every observable can be viewed as coupling the theory to some external system. Famously, such interactions will (generically) break 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.

In 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, generating a "homotopical" generalization of a Lie algebras in any QFT. These "homotopical" Lie brackets are highly computable (requiring only a first course in QFT to compute) and contain familiar information such as anomalies and Operator Product Expansion coefficients. Time permitting, I will discuss how these brackets are even more strongly constrained in holomorphic/topological theories, and prove the absence of perturbative corrections to HT theories with more than one topological direction. Based on arXiv:2403.13049.

### About Particle Physics Theory seminars

The Particle Physics Theory seminar is a weekly series of talks reflecting the diverse interests of the group. Topics include analytic and numerical calculations based on the Standard Model of elementary particle physics, theories exploring new physics, as well as more formal developments in gauge theories and gravity..