Quantum Fields and Strings

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.

In this talk, I will show that the action of soft graviton operators generates a w(1+infinity) symmetry in gravitational theories minimally coupled to massless and massive scalar matter in 4D asymptotically flat spacetimes.  I will discuss how the symmetry action follows from an infinite tower of soft graviton theorems in momentum space.  By generalizing the previous analyses of w(1+infinity) symmetry in massless amplitudes, these results clarify that the symmetry emerges in 4D asymptotically flat gravitational theories without any additional technical ingredients.  This talk is based on a forthcoming paper with Monica Pate. 

Zoom link:  https://pitp.zoom.us/j/91448920819?pwd=cFY0L1JPVFF2bDUwc3JiVlRlbE5ldz09

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.

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.

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

Zoom link:  https://pitp.zoom.us/j/96037678536?pwd=eGdhTWF3UVN1em5uZVpJbWYyM2tzUT09

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.

Recently, powerful quantum field theory techniques, originally developed to calculate observables in colliders, have been applied to describe classical observables relevant to gravitational wave physics. This has motivated a proliferation of approaches to extract classical information from quantum scattering amplitudes. Since the double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory,  in this talk I will first discuss scattering in Yang-Mills theory as a toy model to study the connection between the framework by Kosower-Maybee-O'Connell (KMOC), the language of effective field theory (EFT) and the eikonal phase. After a brief review of the KMOC formalism to compute classical observables from scattering amplitudes, I will consider the dynamics of colour-charged particle scattering and explain  how to compute the change of colour, and the radiation of colour, during a classical collision. Finally, moving on to gravity, I will discuss the deflection of light by a massive spinless/spinning object using the novel worldline quantum field theory (WQFT) formalism for classical scattering.

Zoom link:  https://pitp.zoom.us/j/98649931693?pwd=Z2s1MlZvSmFVNEFqdjk2dlZNRm9PQT09

The background geometry seen by a propagating string in the non-relativistic limit is non-Lorentzian. This motivates us to study the non-relativistic AdS/CFT correspondence as a new example of non-AdS holography. In this talk I will focus on the string side of the correspondence, keeping an integrability perspective, and illustrate remarkable differences from the relativistic theory. I will report on recent progress made in AdS5xS5 non-relativistic strings, in particular regarding their classical string solutions, semi-classical expansion of the action, coset space formulation of the action, Lax pair and some preliminary progress on the spectral curve. Based on work done in collaboration with J. M. Nieto, O. Ohlsson Sax, A. Torrielli, S. Van Tongeren. 

Zoom link:  https://pitp.zoom.us/j/99895811528?pwd=YWIreWtzdmRBanpIZXBLLzY3ZFNoZz09

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.

In general, observables in QFTs can only be computed perturbatively using Feynman integrals. In this talk, which is based on arXiv:2008.12310 and arXiv:2204.06414, I will address some questions on the computability of such observables. By looking at QFT through the lens of tropical geometry, one can see that the runtime of such computations is dominated by the time it takes to understand the structure of certain polytopes. In the case of scalar QFTs on Euclidean space the relevant polytopes turn out to be generalized permutahedra, whose structure is well-understood thanks to the works of Postnikov, Aguiar and Ardila.  Using these insights, results in a new algorithm for Feynman integral evaluation that exceeds the capabilities of existing methods by multiple orders of magnitude, while being easy to implement.  I will also briefly discuss current wip that extends these findings to QFTs on Minkowski spacetime.

Zoom link:  https://pitp.zoom.us/j/93629580865?pwd=WnJ6aUVpckFZWGVDL0NqMTFrWlhBQT09

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.

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09