2024 Simons Collaboration on Confinement and QCD Strings Annual Meeting

The second annual meeting of the collaboration took place on November 7–8, 2024 at the Simons Foundation. It was followed by a satellite workshop on November 10–12 at the Princeton Center for Theoretical Science (PCTS), where many additional talks and discussions took place: https://pcts.princeton.edu/events/2024/pcts-simons-collaboration

The PCTS workshop included nine shorter talks presented by some of the graduate students and post-docs. This workshop provided an excellent follow-up to the second annual meeting, and it was very helpful that the two were within an easy trip from each other.

The workshops have continued developing the main themes of the collaboration, which include the dynamics of confining flux tubes (talks by Teper, Caselle, Gorbenko, Komargodski), the role of vortices and monopoles in the confinement mechanisms of various models (Teper, Unsal, Dumitrescu), and detailed studies of 2D models of confinement (Tarnopolsky, Dempsey, Popov). The connections between quantum simulation and computation, and the Hamiltonian lattice models in 1+1 and 2+1 dimensions, were discussed actively during the PCTS workshop. This was thanks to the excellent talks by two leading experts, Martin Savage and Christian Bauer.

The spectra of long confining strings in pure glue gauge theory are known to be approximately described by the Nambu-Goto action, but the subtle and model dependent higher-derivative corrections are known to be present. The talks by Michael Teper and Michele Caselle presented the latest numerical results on various 3D gauge theories including Z(N), U(1), and the non-Abelian examples with few colors. In all these models, the correction to the energy of the confining string wrapped around the circle of radius R scales as 1/R7 and the coefficient of this term, which is model-dependent, was calculated with excellent accuracy. The role of vortices and monopoles in the lattice theory with gauge group Z(N), which is the center of SU(N), was discussed by Teper. Gorbenko showed how Yang-Mills theory in anti-de Sitter space can be used to study the dynamics of flux tubes in the dual boundary theory, while Aharony discussed new ideas for the phase diagram of the supersymmetric 3D gauge theory.

In terms of the real-world applications of theoretical ideas, Komargodski presented new results on the effective theory of string junctions in various models including the holographic ones, while Ian Moult showed how the energy correlators measured at LHC can be used to explore the transition from asymptotic freedom to confinement. Cherman discussed the Aharonov-Bohm phases which play an important role in theories containing the axionic strings, while Venugopalan discussed the role of chiral anomaly in deep inelastic scattering.

Minahan discussed a precision calculation of the Hagedorn temperature, related to appearance of a tachyonic model on a string wound around the thermal direction, using the integrability of the N=4 supersymmetric Yang-Mills theory. Komatsu applied the methods of integrability to calculations of correlation functions on the Coulomb branch of this gauge theory.

Gauge theory in 1+1 dimensions has been an important source of information and intuition about non-perturbative gauge dynamics. The Schwinger model has been a valuable toy model for QCD since the 1970s, when the bosonization approach led to many new results. Tarnopolsky talked about the Hamiltonian lattice approach to the Schwinger model with staggered fermions, where an improvement term (a mass shift) uncovered two years ago has led to much faster convergence to the continuum limit. As a demonstration of this, Tarnoposky determined to several significant digits the critical value of mass over charge where the low-energy dynamics is in the Ising universality class. He showed that this critical value deviates very slightly from 1/3. In order to achieve an accuracy this high, he carefully studied the symmetries of the model on an open chain and the spectrum of boundary operators. Tarnopolsky and collaborators have developed new software for studying the tensor networks that has allowed them to work with up to 1000 qubits and achieve the new level of precision.

A 2D model which has some similarities with the Schwinger model, but has richer dynamics and is more similar to 4D QCD, is the 2D SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions. It is attracting renewed interest because of its connection with string theory and because it may be the simplest non-Abelian model which exhibits (when the fermions are massive) a mass gap and an area law for the Wilson loop in the fundamental representation. Speaking at PCTS, Ross Dempsey presented the Hamiltonian lattice gauge theory formulation of adjoint QCD2 with arbitrary gauge group, as well as numerical results for SU(2) and SU(3). This lattice model contains the topologically non-trivial sectors, and the degeneracies between them appearing in the massless model are known to be a consequence of non-invertible symmetry of the continuum theory. Extrapolation of the numerical lattice results to the continuum limit, which is quite precise when the spatial circle is small, indeed suggests the presence of the degeneracies. Dempsey also showed that the lattice adjoint QCD2 possesses a Goldstino mode on the confining string at the supersymmetric value of the adjoint fermion mass.

A number of speakers at PCTS (Lin, Yaffe, Jevicki, Sandor) discussed various new approaches, mostly numerical, to large N models in the ‘t Hooft limit. These approaches promise to shed new light on the dynamics of large N gauge theory in various dimensions. The total number of participants in the back-to-back workshops was over 100, and they have expressed a high level of satisfaction with the two events. The collaboration looks forward to the several workshops, which will be held in 2025.

Ofer Aharony
Weizmann Institute

The Phase Diagram of QCD in 2+1 Dimensions

In this talk, Ofer Aharony will discuss what is known about the phase diagram of QCD, the SU(N) gauge theory with Nf Dirac fermions in the fundamental representation, with equal masses for simplicity. Aharony will begin by reviewing what is known in 3+1 dimensions, focusing on the low-energy limit of the massless theory in the large N, Nf limit, and on the conformal field theories it sometimes flows to. Aharony will then move on to 2+1 dimensions, and discuss the phase diagram as a function of the mass and the discrete parameters N, Nf and the Chern-Simons level k, focusing again on the limit of large N, Nf and k. For some range of parameters, a conformal field theory (corresponding to a second order phase transition when changing the mass) appears at low energies, while for other ranges of parameters, there are one or more first order phase transitions. Ofer Aharony will discuss various scenarios for how conformality can be lost as one moves in this parameter space. Based on work in progress with Thomas Dumitrescu, Zohar Komargodski and Jiangyuan Qian.
 

Michele Caselle
Torino University

Recent Results on the Effective String Description of Confinement
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In this talk, Michele Caselle will first give a brief introduction to the effective string model. Caselle will then discuss a few recent results on the behavior of the string in the vicinity of the deconfinement transition obtained with a combination of analytical tools and Monte Carlo simulations.
 

Aleksey Cherman
University of Minnesota

Periodic Couplings, Aharonov-Bohm Phases and QCD Axions
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Aleksey Cherman will discuss periodic coupling parameters that can appear in effective field theories with multiple \(U(1)\) global symmetries. These couplings can lead to interesting Aharonov-Bohm phases. As an example, such couplings can appear when QCD is coupled to an axion, and they induce Aharonov-Bohm phases for baryons moving around axion strings.
 

Matthias Gaberdiel
ETH Zurich

Progress on AdS3/CFT2
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Matthias Gaberdiel will describe recent progress with aspects of the AdS3/CFT2 duality. Among other things, Gaberdiel will explain the exact tensionless string duality for the case of AdS3 x S3 x S3 x S1 and will also show how the string excitations associated to AdS3 & S3 emerge naturally from the symmetric orbifold perspective.
 

Victor Gorbenko
EPFL Lausanne

Defects: Quantum Groups and Confinement
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The talk will consist of two parts unified by the study of operators that live on defect lines. In the first part, Victor Gorbenko will discuss quantum field theories that have quantum group as a global symmetry. Gorbenko will show that quantum groups act naturally on defect ending operators and even can transform a local operator into a defect ending one. Gorbenko will focus on a particular solvable 2D quantum field theory where the symmetry generators can be constructed explicitly. It turns out that part of quantum group symmetry in this model is in a certain sense confined. In the second part, the talk will cover different defects, the confining flux tubes of Yang-Mills theory.

To use powerful techniques available for conformal defects, we will place Yang-Mills on AdS geometry with Neumann boundary conditions. This way, a long confining flux tube in d+1 dimensional Yang-Mills is described by a Wilson line in the boundary d-dimensional conformal theory. The displacement operator of the defect corresponds to the branon that lives on the worldsheet of the flux tube. This defect is perturbative when the AdS radius is small, and at large radius, it becomes equivalent to the flat space flux tube described by the effective string theory.
 

Grigory Tarnopolsky
Carnegie Mellon University

Precise Numerical Analysis of the Schwinger Model Near Criticality
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In this talk, Grigory Tarnopolsky will discuss recent results from the numerical analysis of the massive Schwinger model at criticality. Using the tensor networks code recently developed by our group, we were able to efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 1,000 qubits. As a result, we have performed a precise computation of the critical mass of the Schwinger model using various “criticality criteria” and have observed perfect agreement.
 

Michael Teper
Oxford University

Confinement in Z(N) and U(1) Lattice Gauge Theories in 2+1 Dimensions
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Z(N), the center of SU(N), has often been suggested as playing a central role in color confinement. We investigate the confining properties of Z(N) lattice gauge theories in 2+1 dimensions. We compare the spectrum of closed flux tubes to the GGRT string spectrum, and we explore the role of monopole-instantons and closed flux loops as order parameters for the confining phase and the small volume/high temperature deconfined phases. We carry out our calculations in the gauge theory rather than in the dual spin models, just as one does in non-Abelian lattice gauge theories.
 

Raju Venugopalan
Brookhaven National Laboratory & Stony Brook University

The Role of the Chiral Anomaly in Polarized Deeply Inelastic Scattering: Topological Screening and Sphaleron Transitions
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The chiral anomaly has long been understood to play a key role in polarized deep inelastic scattering, directly relating physics at high and low momentum transfer. For example, as shown by Veneziano and collaborators, the proton’s quark helicity is directly proportional to the topological susceptibility of the QCD vacuum. We employ a powerful worldline formalism to describe the rich interplay of the low energy Wess-Zumino-Witten dynamics with that of spinning partons with striking consequences. In particular, we argue that future polarized DIS measurements at the Electron-Ion Collider may provide first evidence of sphaleron transitions in nature.