Institut des Hautes Etudes Scientifiques (IHES) · Video summary

Clay Cordova - Electron-Monopole Scattering from Conformal Field Theory

This talk explores electron-monopole scattering using conformal field theory, revealing how twisted sectors are crucial for understanding unitarity and resolving long-standing puzzles like the K"allen-Lehmann problem.

Institut des Hautes Etudes Scientifiques (IHES) · March 16, 2026 · 70-min episode · 5-min read

Clay Cordova - Electron-Monopole Scattering from Conformal Field Theory

Key takeaways

💡Magnetic monopoles are ubiquitous in UV completions of gauge theories and quantum gravity, implying magnetic charges must become dynamical at some scale.01:01
🎯The presence of a monopole creates fermion zero modes with specific angular momentum and chirality properties, which are sensitive to the monopole's core and crucial for scattering calculations.04:04
🚀Scattering into 'twisted sectors' (Hilbert space sectors not created by local operators) is necessary to fully describe the S-matrix and preserve unitarity when dealing with monopoles.07:35
📚Familiarize yourself with the concept of 'twisted sectors' in conformal field theory to understand how they impact scattering processes involving topological defects.07:35
🔍The problem can be reduced to a 1+1D conformal field theory on a half-space, where the monopole acts as a boundary condition for the fermions.11:16
🔑The Cardy condition (modular invariance on an annulus) provides a powerful, non-linear constraint to explicitly determine boundary states in 1+1D CFTs, essential for calculating correlation functions.23:50

Chapters

0:55✨ Introduction and Motivation
1:49🧲 The Infinite Mass Monopole Model
3:50🌀 Fermion Zero Modes
5:50❓ The S-Matrix Challenge
7:30↔️ Twisted Sectors in Scattering
11:12⬇️ Reduction to 1+1D
13:06🚧 Monopole as a Boundary Condition
14:53📜 Characterizing Boundary Conditions
18:05⚖️ Maximal Flavor Symmetry Boundary Conditions
21:08📐 Explicit Diagonal and Anti-diagonal Boundary Conditions
23:31♾️ Cardy's Modular Technique
29:39💡 Bozonization for Simplicity
32:13🔢 Bosonic Boundary Condition Matrix R
36:45📈 Twisted Sector Correlation Functions
41:32🔗 Modular Invariance and Overlaps
46:31🧮 Calculating the S-Matrix
49:01💯 Unitarity and S-Matrix Results
51:23❓ Open Questions and Future Directions
52:52🤔 Discussion on Solved Problems
1:01:54🔬 Experimental Implications

The digest

Electron-Monopole Scattering from Conformal Field Theory

This presentation explores the complex problem of electron-monopole scattering by reformulating it within the framework of 1+1 dimensional conformal field theory (CFT). The core challenge lies in understanding the scattering of massless charged particles off of a magnetic monopole, particularly addressing the "Kalen-Rubikov problem" which arises from unpaired fermionic zero modes and the difficulty in defining a consistent scattering matrix. The work proposes that by considering "twisted sectors" of Hilbert space and leveraging modular invariance in CFT, a consistent and unitary S-matrix can be computed, resolving this long-standing puzzle.