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Nonperturbative Methods in Quantum Field Theory
from
Monday, May 23, 2022 (9:00 AM)
to
Friday, June 3, 2022 (7:00 PM)
Monday, May 23, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Attacking the SinhGordon model with relativistic continuous matrix product states*

Antoine Tilloy
(
Mines ParisTech
)
Attacking the SinhGordon model with relativistic continuous matrix product states*
Antoine Tilloy
(
Mines ParisTech
)
10:00 AM  11:00 AM
Room: 503/1001  Council Chamber
The SinhGordon model is a 1+1 dimensional quantum field theory with a potential cosh(b phi) that is quite peculiar. It is at the same time exactly solvable (for many observables) and not well understood. I will present the results of a variational exploration of its strong coupling regime with a recent generalization of continuous matrix product states. The advantage of this method is that it does not require introducing a cutoff, UV or IR, is fully nonperturbative, typically converges fast for Hamiltonians with polynomial interactions, and gives rigorous energy upper bounds. Its application to the SinhGordon model is only partly successful: observables can be computed accurately up to fairly large values of the coupling, but the ultra strong coupling regime remains difficult to access without extrapolations. As a result, the behavior near the selfdual point is not yet fully settled. I will show the basics of relativistic continuous matrix product states, explain how they typically work for phi^4 like theories or even the easier SineGordon model and finally discuss my attempts at taming SinhGordon.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Renormalons from Integrability: A resurgent insight into QFT's conundrum*

Tomas Reis
(
University of Geneva
)
Renormalons from Integrability: A resurgent insight into QFT's conundrum*
Tomas Reis
(
University of Geneva
)
2:00 PM  3:00 PM
Room: 503/1001  Council Chamber
Renormalons are nonperturbative effects which are manifested in perturbative series. While they figure in asymptotically free field theories including both QCD and some integrable models, they are in general poorly understood. In this talk I will present results on how to analytically find these nonpertubative effects in the free energy of integrable models. These effects turn out to defy standard expectations which went back to Parisi and ’t Hooft. I will also present a short introduction to the framework of resurgence and to how it is a key tool in the analysis of nonperturbative effects in QFT.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
Tuesday, May 24, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Hamiltonian truncation in AdS*

Matthijs Hogervorst
(
EPFL
)
Hamiltonian truncation in AdS*
Matthijs Hogervorst
(
EPFL
)
10:00 AM  11:00 AM
Room: 503/1001  Council Chamber
Antide Sitter spacetime is interesting for many reasons: of course it furnishes a canvas for the study of quantum gravity, but it also appears to be a fruitful setting for Hamiltonian truncation. After all, QFTs in AdS have a notion of conserved energy, their Hilbert spaces are wellunderstood, and even a hard energy cutoff preserves many spacetime symmetries. In this talk I will discuss this framework in detail and present some results on both scalar fields and 2d minimal models. In particular, I will discuss the issue of divergent counterterms that arise from the curvature of AdS, and present a prescription to extract the correct continuum limit. Based on work with M. Meineri, J. Penedones and K. Salehi Vaziri, arXiv:2104.10689. An introductory example in Python can be found at the attached link.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Torus Spectroscopy: A novel numerical tool to diagnose the nature of quantum phase transitions and quantum spin liquids

Andreas Laüchli
(
PSI / EPFL
)
Torus Spectroscopy: A novel numerical tool to diagnose the nature of quantum phase transitions and quantum spin liquids
Andreas Laüchli
(
PSI / EPFL
)
2:00 PM  3:00 PM
Room: 503/1001  Council Chamber
In this talk I will present the torus spectroscopy, i.e. the analysis of the finite volume spectrum of the Hamiltonian on a spatial torus in 2+1D as a practical numerical tool to determine the universality class of quantum phase transitions. We show an application with an emergent 3D O(2) phase transition and that we are able to detect the presence of dangerously irrelevant couplings. In a second application we report on ongoing work to shed light on the possible presence of a QED$_3$ like phase (Dirac spin liquid) in a frustrated spin model.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
4:00 PM
Structured Discussion
Structured Discussion
4:00 PM  5:30 PM
Room: 503/1001  Council Chamber
Wednesday, May 25, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Hydrodynamization, asymptotics and the early to late time interpolation in relativistic hydrodynamics*

Inês Aniceto
(
University of Southampton
)
Hydrodynamization, asymptotics and the early to late time interpolation in relativistic hydrodynamics*
Inês Aniceto
(
University of Southampton
)
10:00 AM  11:00 AM
Room: 503/1001  Council Chamber
Dissipative relativistic hydrodynamics is expected to describe the late times, thermalised behaviour of strongly coupled fluids such as a strongly coupled super YangMills plasma. These systems are then accurately described by a hydrodynamic series expansion in small gradients. Surprisingly, this hydrodynamic expansion is accurate even when the systems are still quite anisotropic: the nonhydrodynamic modes governing the nonequilibrium behaviour at very earlytimes become exponentially close to the hydrodynamic solution in an early process called hydrodynamization. This early success is intimately related with the fact that the hydrodynamic expansion is asymptotic. The theory of transseries and resurgence explicitly shows how the nonhydrodynamic modes are in fact encoded in this latetime expansion. In this talk we will focus on a MIStype model and use exponentially accurate summations of the the latetime resurgent transseries to recover the behaviour of the fluid before hydrodynamisation, and effectively match it to any given initial nonequilibrium condition. We will further show that such summations can provide analytic predictions beyond the late time regime.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
No Talk Scheduled (CERN Theory Colloquium)
No Talk Scheduled (CERN Theory Colloquium)
2:00 PM  3:00 PM
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
4:00 PM
Hamiltonian truncation for real time dynamics in (gauge) QFT*

Ivan Kukuljan
(
Max Planck Institute for Quantum Optics
)
Hamiltonian truncation for real time dynamics in (gauge) QFT*
Ivan Kukuljan
(
Max Planck Institute for Quantum Optics
)
4:00 PM  5:00 PM
Room: 503/1001  Council Chamber
Hamiltonian truncation methods represent a powerful toolbox for a set of problems that are otherwise very challenging in strongly coupled quantum field theory: nonequilibrium physics and real time evolution. In many such cases analytical approaches are limited as well as numerical tools like lattice gauge theory and tensor networks. I will talk about recent developments in this field with emphasis to entanglement properties of QFT, connection to ultra cold atomic simulators and exploring new fundamental phenomena.
Thursday, May 26, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Hamiltonian Truncation and Effective Field Theory*

Kara Farnsworth
(
Case Western Reserve University
)
Hamiltonian Truncation and Effective Field Theory*
Kara Farnsworth
(
Case Western Reserve University
)
10:00 AM  11:00 AM
Room: 500/1001  Main Auditorium
Hamiltonian truncation is a nonperturbative numerical method for calculating observables of a quantum field theory by truncating the Hilbert space to states with energy below a maximum energy cutoff. In this talk I will present an effective field theory approach to Hamiltonian truncation, which provides a systematic way of improving the calculations without increasing the energy cutoff. I will demonstrate this with numerical results for the two dimensional phi^4 theory, and talk about future applications of this method to more complicated theories.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
3:00 PM
Thermalization and Chaos in 1+1d QFTs

Luca Delacrétaz
(
University of Chicago
)
Thermalization and Chaos in 1+1d QFTs
Luca Delacrétaz
(
University of Chicago
)
3:00 PM  4:00 PM
Room: 500/1001  Main Auditorium
Nonintegrable QFTs are expected to thermalize and exhibit emergence of hydrodynamics and chaos. In weakly coupled QFTs, kinetic theory captures local thermalization; such a versatile tool is absent away from the perturbative regime. I will present analytical and numerical results using nonperturbative methods to study thermalization at strong coupling. I will show how requiring causality in the thermal state leads to strong analytic constraints on the thermodynamics and out of equilibrium properties of any relativistic 1+1d QFT. I will then discuss Lightcone Conformal Truncation (LCT) as a powerful numerical tool to study thermalization of QFTs. Applied to $\phi^4$ theory in 1+1d, LCT reveals eigenstate thermalization and onset of random matrix universality at any nonzero coupling. Finally, I will discuss prospects for observing the emergence of hydrodynamics in QFTs using Hamiltonian truncation.
4:00 PM
Coffee Break
Coffee Break
4:00 PM  4:30 PM
4:30 PM
Structured Discussion
Structured Discussion
4:30 PM  6:00 PM
Room: 500/1001  Main Auditorium
Friday, May 27, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
PostQuantum Quench Growth of Renyi Entropies in Perturbed Luttinger Liquids

Robert Konik
(
Brookhaven National Laboratory
)
PostQuantum Quench Growth of Renyi Entropies in Perturbed Luttinger Liquids
Robert Konik
(
Brookhaven National Laboratory
)
10:00 AM  11:00 AM
Room: 500/1001  Main Auditorium
The growth of Renyi entropies after the injection of energy into a correlated system provides a window upon the dynamics of its entanglement properties. We provide here a scheme by which this growth can be determined in Luttinger liquids systems with arbitrary interactions, even those introducing gaps into the liquid. This scheme introduces the notion of a generalized mixed state Renyi entropy. We show that these generalized Renyi entropies can be computed and provide analytic expressions thereof. Using these generalized Renyi entropies, we provide analytic expressions for the short time growth of the second and third Renyi entropy after a quantum quench of the coupling strength between two Luttinger liquids, relevant for the study of the dynamics of cold atomic systems. For longer times, we use truncated spectrum methods to evaluate the postquench Renyi entropy growth.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Multiparticle observables from a finite Euclidean spacetime*

Maxwell Hansen
(
University of Edinburgh
)
Multiparticle observables from a finite Euclidean spacetime*
Maxwell Hansen
(
University of Edinburgh
)
2:00 PM  3:00 PM
Room: 500/1001  Main Auditorium
Numerical calculations using latticeregularized QFTs are a powerful tool to understand nonperturbative systems when analytic methods are unavailable. However, the utility of numerical results can be affected by two issues: (i) calculations are necessarily performed in a finitevolume spacetime and (ii) Euclidean (rather than Minkowski) signature correlation functions are evaluated. Both aspects play an especially important role for multiparticle observables including scattering and decay amplitudes and inclusive rates. In this talk, I will discuss progress in extracting such observables from numerical lattice field theory, based on two strategies. One is to use the finitevolume as a tool, rather than an unwanted artefact, and to apply generic field theoretic relations between finitevolume quantities and infinitevolume amplitudes. The second is to carefully regulate the inverse Laplace transform, in order to estimate Minkowski observables directly from numerical Euclidean correlators.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
Saturday, May 28, 2022
Sunday, May 29, 2022
Monday, May 30, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Hamiltonian Formulations of Lattice Gauge Theories, with an eye towards Quantum Simulation*

Dorota Grabowska
(
CERN
)
Hamiltonian Formulations of Lattice Gauge Theories, with an eye towards Quantum Simulation*
Dorota Grabowska
(
CERN
)
10:00 AM  11:00 AM
Room: 500/1001  Main Auditorium
There are many fundamental questions in particle and nuclear physics that cannot be addressed via classical computing techniques. These include the equation of state for finite density nuclear matter, realtime dynamics of quantum field theories from firstprinciples and nonperturbative aspects of chiral gauge theories. In recent years quantum computing hardware has seen dramatic advancements, which have brought with them the possibility to apply quantum computing to these and other open problems in high energy physics. In this talk, after a brief introduction to quantum computing, I will discuss my recent work towards the quantum simulation of lowerdimensional lattice gauge theories, focusing on the interplay between Gauss’ law, gauge redundancies and (un)favourable resource scaling.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Nonequilibrium dynamics in 1+1 dimensional interacting scalar quantum field theory*

Gábor Takács
(
Budapest University of Technology and Economics
)
Nonequilibrium dynamics in 1+1 dimensional interacting scalar quantum field theory*
Gábor Takács
(
Budapest University of Technology and Economics
)
2:00 PM  3:00 PM
Room: 500/1001  Main Auditorium
We develop a truncated Hamiltonian method to investigate the dynamics of the 1 +1dimensional ϕ^4 theory following quantum quenches. The results are compared to two different semiclassical approaches, the selfconsistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We then use this method to investigate the decay by realising it as a quantum quench, and show that in the thin wall limit the theoretical prediction is well reproduced for several values of the coupling in a range of the value of the latent heat, apart from a normalisation factor which only depends on the strength of selfinteractions.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
Tuesday, May 31, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
A nonperturbative Smatrix from truncation*

Jedidiah Thompson
(
Stanford University
)
A nonperturbative Smatrix from truncation*
Jedidiah Thompson
(
Stanford University
)
10:00 AM  11:00 AM
Room: 500/1001  Main Auditorium
Recent advances in Hamiltonian truncation have demonstrated it to be a useful tool for obtaining nonperturbative information about quantum field theories, even in the stronglycoupled regime. One particularly exciting feature of this technique is that it can be formulated in Minkowski rather than Euclidean space, making it easier to calculate realtime quantities. Truncation is particularly suited to obtaining spectral information (particle masses, operator spectral densities, etc.), but these are not the only observables of interest, especially when trying to make contact with highenergy experiments. I will explain how to use approximate knowledge of a QFT’s energy eigenstates to compute amplitudes for particle scattering, which can in turn be used to compute cross sections and decay rates. I will demonstrate this technique with an example of lightcone conformal truncation for the O(N) model in 2+1d at strong coupling, but it is worth emphasizing that the method can work with any numerical technique that outputs information about approximate Hamiltonian eigenstates. Along with the amplitude in the physical region, I will show that it is possible to analytically continue to the entire complex Mandelstam plane, and in fact that numerical convergence can be even better away from the physical region.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Hamiltonian Truncation with Larger Dimensions

Joan Elias Miró
(
ICTP
)
Hamiltonian Truncation with Larger Dimensions
Joan Elias Miró
(
ICTP
)
2:00 PM  3:00 PM
Room: 500/1001  Main Auditorium
Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory nonperturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension ∆. In this talk I will review the HT techniques and emphasise few key open problems. I will also discuss the recent efforts to extend these ideas to higher dimensions (d > 2) and for UV divergent relevant operators (d/2 <= ∆ < d).
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
4:00 PM
Structured Discussion
Structured Discussion
4:00 PM  5:30 PM
Room: 500/1001  Main Auditorium
Wednesday, June 1, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Conformal Colliders Meet the LHC*

Ian Moult
(
Yale University
)
Conformal Colliders Meet the LHC*
Ian Moult
(
Yale University
)
10:00 AM  11:00 AM
Room: 503/1001  Council Chamber
Jets of hadrons produced at highenergy colliders provide experimental access to the dynamics of asymptotically free quarks and gluons and their confinement into hadrons. Motivated by recent developments in conformal field theory, we show that questions of interest in collider physics can be reformulated as the study of correlation functions of a specific class of lightray operators and their associated operator product expansion (OPE). We show that multipoint correlation functions of these operators can be measured in real LHC data, allowing us to experimentally verify both the scaling properties associated with the OPE, and the celestial block decomposition of higher point correlators.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Tensor Networks: entanglement and the simulation of quantum manybody problems

Mari Carmen Bañuls
(
Max Planck Institute for Quantum Optics
)
Tensor Networks: entanglement and the simulation of quantum manybody problems
Mari Carmen Bañuls
(
Max Planck Institute for Quantum Optics
)
2:00 PM  3:00 PM
Room: 503/1001  Council Chamber
*Theory Colloquium* The term Tensor Network States (TNS) designates a number of ansatzes that can efficiently represent certain states of quantum manybody systems. In particular, ground states and thermal equilibrium of local Hamiltonians, and, to some extent, real time evolution can be numerically studied with TNS methods. Quantum information theory provides tools to understand why they are good ansatzes for physically relevant states, and some of the limitations connected to the simulation algorithms. Originally introduced in the context of condensed matter physics, these methods have become a stateoftheart technique for strongly correlated onedimensional systems. Their applicability extends nevertheless to other fields. As an example, in the last few years it has been shown that TNS are also suitable to study lattice gauge theories and other quantum field problems. This talk gives an overview of the possibilities and limitations of these methods, and some of their recent applications to this kind of problems.
3:00 PM
Coffee Break
Coffee Break
3:00 PM  3:30 PM
4:00 PM
Adiabatic continuity, TQFT couplings, and calculable confinement

Mithat Ünsal
(
North Carolina State University
)
Adiabatic continuity, TQFT couplings, and calculable confinement
Mithat Ünsal
(
North Carolina State University
)
4:00 PM  5:00 PM
Room: 503/1001  Council Chamber
I will describe the idea of adiabatic continuity which can be used to continuously connect strongly coupled gauge theories on R^4 to compactified gauge theories on two setups: R^3 x S^1 and R^2 x T^2. Recall that in standard (thermal) compactifications, there are generically phase transitions. But in the last 15 years, we learned how to go around them and move to weak coupling regimes without phase transitions by employing nonthermal boundary conditions, doubletrace operators or more recently 't Hooft flux backgrounds. In the weak coupling regime, properties such as confinement, chiral symmetry breaking, and multibranch structure as a function of theta angle are semiclassically calculable. As opposed to common beliefs emanating from the 70s, which emphasize that these are necessarily strong coupling phenomena, all of them can be realized in weak coupling regimes. I will briefly mention the roles of fractional instantons, resurgence, Lefschetz thimbles, and TQFT couplings, and state some open problems. The presentation will be at the colloquium level.
Thursday, June 2, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Confinement versus 1form symmetries at large N*

Aleksey Cherman
(
University of Minnesota
)
Confinement versus 1form symmetries at large N*
Aleksey Cherman
(
University of Minnesota
)
10:00 AM  11:00 AM
Room: 500/1001  Main Auditorium
There are two known ways to tie quark confinement to symmetries: one way (the older one) in terms of "center symmetry", and the other one (the newer one) is in terms of a "1form symmetry". By now it is widely accepted that the new idea of 1form symmetry, which is based on the existence of codimension2 topological operators, is a generalization of the old idea of center symmetry. I'll explain how large N QCD poses a sharp challenge to this notion. It enjoys selection rules that can be explained by center symmetry, but not by 1form symmetry. I'll explain how these selection rules can be deduced from the properties of certain unconventional topological operators.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Aspects of Numerical Bootstrap*

Yuan Xin
(
Yale University
)
Aspects of Numerical Bootstrap*
Yuan Xin
(
Yale University
)
2:00 PM  3:00 PM
Room: 500/1001  Main Auditorium
My talk consists of two parts. In the first part, I will discuss a conformal bootstrap study of three dimensional Quantum Electrodynamics coupled to four flavors of electrons. The model is a classic example of a strongly coupled gauged quantum field theory and is believed to have a conformal lowenergy phase, while its critical parameters lacks a conclusive answer. We find that the scaling dimensions of the lowestcharge monopole operator and the adjoint fermion bilinear operator can be bounded in a closed region after implementing spectrum assumptions inspired by the largeN_f perturbative predictions. Bootstrap constraints on the conserved current central charges are comfortably consistent with largeN_f perturbation theory, suggesting that at least part of the largeN_f perturbative predictions form a consistent solution to crossing. I will discuss the validity of the assumptions we used and compare with lattice simulations and previous bootstrap study results. In the second part, I will introduce a new method utilizing a crossing equation in Quantum Mechanics to bound spectrum and matrix elements of any theory with a specific Hamiltonian. The new method is inspired by the method of bootstrapping matrix model using the matrix positivity. I will show that this method provides precision solution to a toy example — Anharmonic Oscillator, and suggest a generalization to study infinitevolume spin chains.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM
4:00 PM
Structured Discussion
Structured Discussion
4:00 PM  5:30 PM
Room: 500/1001  Main Auditorium
Friday, June 3, 2022
9:30 AM
Coffee Break
Coffee Break
9:30 AM  10:00 AM
10:00 AM
Bootstrapping the aanomaly in 4d QFTs*

Denis Karateev
(
University of Geneva
)
Bootstrapping the aanomaly in 4d QFTs*
Denis Karateev
(
University of Geneva
)
10:00 AM  11:00 AM
Room: 503/1001  Council Chamber
I will discuss 4d scattering amplitudes in UV complete quantum field theories (QFTs). I will show how the aanomaly describing its UV fixed point is related to parameters describing the scattering amplitude via unitarity. I will then present various numerical nonperturbative bounds.
12:00 PM
Lunch
Lunch
12:00 PM  2:00 PM
2:00 PM
Bootstrapping photon scattering in 3+1d*

Aditya Hebbar
(
École Polytechnique
)
Bootstrapping photon scattering in 3+1d*
Aditya Hebbar
(
École Polytechnique
)
2:00 PM  3:00 PM
Room: 503/1001  Council Chamber
The Smatrix bootstrap is a program where one uses the general principles of analyticity, crossing symmetry and unitarity of scattering amplitudes to study the allowed space of quantum field theories. In this talk I will consider the two photon to two photon scattering amplitude and explain how we can use numerical Smatrix bootstrap methods to derive nonperturbative bounds on Wilson coefficients in the low energy effective field theory expansion of photons.
3:30 PM
Coffee Break
Coffee Break
3:30 PM  4:00 PM