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Quantum field theories, strong coupling, and duality: Introduction Part 2

Event Category:
Joint Math/Physics Seminar
Speaker:
Ben Heidenreich
Institution:
UMass Amherst Physics

Progress in understanding quantum field theories (QFTs) is hindered by the fact that the vast majority of them involve strongly-coupled dynamics at some (or all) length scales. Duality is a powerful (though not fully systematic) tool for understanding these strong dynamics, especially in the case of supersymmetric QFTs. I briefly survey the "universe" of known quantum field theories and some of the dualities that can be used to explore it. Many of these dualities are intimately connected with various areas of mathematics, and I try to highlight these connections wherever possible, without going into detail.

With this context in mind, I then focus on the expansive "class S" construction, which provides a systematic picture of the dualities within a large class of four-dimensional QFTs with half-maximal supersymmetry by relating them to a particular set of "parent" six-dimensional conformal field theories (CFTs) with twice as much supersymmetry. These parent theories admit an ADE classification, and the class S construction involves a choice of ADE algebra together with a choice punctured Riemann surface, where each puncture is decorated by a certain kind of label (a Young diagram with n+1 boxes in the A_n case). The different dual descriptions of the resulting four-dimensional QFT then correspond to different pants decompositions of the punctured Riemann surface in question.

This second part of my introductory talk continues to set the stage for the math/physics seminar series this semester, and is aimed at graduate students in either field. Technical details will be deferred to later talks by other speakers.

As always, graduate students are encouraged to join.

Wednesday, February 22, 2023 - 12:30pm
419B