Quantum Fields and Strings

We consider four-point correlators in an arbitrary excited state of a quantum field theory.  We show that when the theory and state are holographic, such correlators can produce high-quality movies of point-like bulk particles, revealing the geometry in which they move. In some situations, Einstein’s equations amount to a local differential equation on the correlator data. In theories or states that are not holographic, images are too blurry to extract a bulk geometry. Calculations are performed by adapting formulas from conformal Regge theory, to excited states and out-of-time-order correlators.

Zoom link: https://pitp.zoom.us/j/94153545930?pwd=YUFsUW44S1Z5Ri83a2xQdEN0Vk9XZz09

One central property of the S-matrix is its invariance under field redefinitions. I will discuss how the geometry of field space makes this invariance manifest. This geometric formulation also has practical consequences. Scattering amplitudes and the renormalization group equations for a theory of scalars and gauge bosons only depend on geometric quantities. Also, the scattering amplitudes satisfy a geometric soft theorem.

Zoom link:  https://pitp.zoom.us/j/98973018515?pwd=MFJFSGM4RS9KRHFOREFBc1gvWXYwQT09

I will speak about my recent work with Vladimir Kazakov where we study the SU(Nc) lattice Yang-Mills theory in the planar limit, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on the maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, the Monte Carlo approach.

Zoom link:  https://pitp.zoom.us/j/96101268796?pwd=QkdJbm9GUzQ2YnIrM1NlcUt2Z3Nvdz09

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.