Search Talks

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

The supersymmetric index of N=4 SU(N) Super Yang-Mills is a well studied quantity. In 2104.13932, using the Bethe Ansatz approach, we analyzed some family of contributions to it. In the large N limit each term in this family has a holographic interpretation - it matches the contribution of a different Euclidean black hole to the partition function of the dual gravitational theory. By taking into account non-perturbative contributions (wrapped D3-branes, similar to Euclidean giant gravitons), we further showed a one to one match between the contributions of the gravitational saddles and this family of contributions to the index, both at the perturbative and non-perturbative levels. I'll end with newer results, concerning the form of these terms at finite N, new solutions to the Bethe Ansatz equations (i.e. additional contributions to the index beyond the ones described in that paper), and some ongoing effort to classify all the solutions to these equations.

Zoom Link: https://pitp.zoom.us/j/95037315617?pwd=ell4WExrSXJ4YUVyaXAzRGJjdjYxUT09

With no hints of dark matter in the "classical WIMP" region of parameter space, experimentalists have begun searching in earnest for low mass (MeV-GeV scale) dark matter. However, efforts to probe this region of parameter space have been hindered by an unexpected and mysterious source of background events, dubbed the "low energy excess." Recently, mechanical stress has been shown to create a "low energy excess"-like source of events, and a microphysical picture of how stress creates this background is emerging. In addition to providing a path forward for low mass dark matter searches, these results may address several outstanding problems limiting the performance of superconducting quantum computers.

Zoom Link:  https://pitp.zoom.us/j/92147233613?pwd=RW5PaUNUZlE3SUNnTlZHaVFrdnV3dz09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

I'll explain work in progress, joint with Miroslav Rapcak, on geometric constructions of vertex algebras associated to divisors in toric Calabi-Yau threefolds, in terms of moduli stacks of objects in certain exotic abelian subcategories of complexes of coherent sheaves on the underlying threefold. These vertex algebras were originally proposed by Gaiotto-Rapcak, and constructed mathematically in the example of affine space by Rapcak-Soibelman-Yang-Zhao, building on Schiffmann-Vasserot's proof of the AGT conjecture. We give a geometric explanation and generalization of the quivers with potential that feature in the latter results, and outline the analogous construction of vertex algebras in this setting.

Zoom link:  https://pitp.zoom.us/j/93749710253?pwd=Y3NUTHBXZ3FPQUdPU0E0d0ttVzFFdz09

I discuss novel symmetries of perturbation theory around rotating and non-rotating black holes in general relativity, and discuss their origins and implications for gravitational-wave astronomy. This is motivated by two special aspects of black hole perturbations in four dimensions: isospectrality of quasinormal modes and the vanishing of tidal Love numbers. There turn out to be off-shell symmetries underlying each of these phenomena. One is a duality, which on shell reproduces the famous Chandrasekhar duality and therefore underlies isospectrality, and can be thought of as an extension of electric-magnetic duality to black hole backgrounds. The other is a set of "ladder symmetries" relating modes of different angular momentum or spin, which imply the vanishing of Love numbers. This has a geometric origin in the conformal symmetry of low-frequency modes.

Zoom link:  https://pitp.zoom.us/j/93633894223?pwd=cEFRYno5WSt5NUJlOWJLdVZHWjE1QT09