2025 Simons Collaboration on Confinement and QCD Strings Annual Meeting

The third annual meeting of the collaboration took place on November 13–14, 2025 at the Simons Foundation. It was preceded by a satellite workshop on November 10–12 at the Simons Center for Geometry and Physics (SCGP), where many additional talks and discussions took place: https://scgp.stonybrook.edu/archives/46158

The SCGP workshop, which was organized by Klebanov, Komargodski, and Venugopalan, nicely complemented the annual meeting, giving an opportunity to many participants to present their work. Participants expressed a high level of satisfaction with the two events, whose highlights are briefly described below.

In the first talk, Klebanov presented an overview of the progress made by the collaboration since its inception. Caselle presented new results on baryon junctions of confining strings in 3D Yang-Mills theory. The numerical results of his group had nice interplay with the analytical work of Komargodski and Zhong, which was presented in Zhong’s talk at SCGP. Aharony previewed his upcoming publication with Dumitrescu on the various mechanisms for ending the conformal window. Dumitrescu presented an analysis of modes around the Abrikosov-Nielsen-Olesen strings, which include a worldsheet axion, while precise new results on the axion in lattice Yang-Mills theory were presented by Athenodorou. Sulejmanpasic and Unsal talked about the role of Z(N) vortices and monopoles in the confinement mechanisms of various models, while the role of fractional instantons was discussed by Tanizaki and Bergner. New numerical results on meson spectra in large N QCD were presented by Bonanno, while the inherently gluonic effects in hadrons were discussed by Shanahan. The quantum simulation and tensor network approaches to gauge theory Hamiltonians were discussed in talks by Itou, Zache, and Pufu. Pufu also discussed progress in adjoint QCD2, including construction of the conserved supercurrent at a special value of fermion mass.

The workshop included various topics in non-perturbative quantum field theory, where new results on defects in free bulk theories were presented by Herzog. The rapidly developing Hamiltonian truncation methods for strongly coupled three-dimensional QFT, which include the fuzzy sphere regulator, were discussed in talks by Katz and Tarnopolsky.
In terms of the real-world applications of theoretical ideas, Sheihing described holographic approaches to heavy quark propagation through the Quark-Gluon Plasma and their comparison with experimental data. Moult presented new precise results on the energy correlators, which demonstrate a transition from the nearly conformal to confining behavior. He also described the remarkable efforts to recover and analyze the old LEP accelerator data from CERN.

Igor Klebanov
Princeton University

Collaboration Overview

Igor Klebanov will review some of the key research accomplishments made by collaboration members so far and describe our plans. They will include continuation of the current projects and addition of new research topics.
 

Ofer Aharony
Weizmann Institute of Science

How Does Confinement Begin? On the Possible End-Points of Conformal Windows

The generalization of QCD to arbitrary numbers of colors \(N_c\) and of massless flavors \(N_f\) has a “conformal window” of values of \(N_f\) where the theory flows to a non-trivial conformal field theory with no confinement, such that, as the number of flavors is decreased, the theory transitions to a confining phase (with chiral symmetry breaking). This transition becomes continuous in the limit of large \(N_f\) and \(N_c\) with a fixed ratio between them, and similar continuous transitions ending “conformal windows” occur also in many other theories.

In this talk, which is a continuation of his talk at last year’s collaboration meeting, Ofer Aharony will describe four general ways (one of which is the popular “merger scenario”) for how such “conformal windows” can end, and present examples where each of them occurs. It is not known which of these scenarios occurs in (large \(N_c\)) QCD, and Aharony will describe how they can be distinguished by precise lattice simulations.
 

Michele Caselle
Torino University

Advanced Simulation Methods for Lattice Gauge Theories and New Results in (2+1) Dimensions

In this talk, Michele Caselle will first discuss a recent proposal to improve the effectiveness of lattice gauge theories (LGTs) simulations by combining non-equilibrium Monte Carlo sampling with machine-learning flows in the so-called stochastic normalizing flows (SNF) algorithm.

In the second part of the talk, Caselle will present a few results we obtained over the past year on the effective string approach to (2+1) dimensional LGTs. In particular, he will present estimates for the mass of the Baryon junction, the behavior of the effective string potential in the U(1) theory and on the intrinsic width of the flux tube in the SU(2) LGT.
 

Silviu Pufu
Princeton University

Precision Studies and Supersymmetry of 2D Adjoint QCD and Its Generalizations

The 1+1-dimensional adjoint QCD theory — namely, SU(N) gauge theory coupled to a Majorana fermion in the adjoint representation of the gauge group — has been a useful model for understanding a variety of gauge theory phenomena in a more tractable setup.

In this talk, Silviu Pufu will describe some recent progress on numerical simulations of this theory involving infinite tensor networks. Afterwards, he will focus on a specific value of the fermion mass where the adjoint QCD theory exhibits supersymmetry. He will describe the construction of a gauge-invariant, Lorentz-covariant supercurrent, whose conservation relies on the presence of a quantum anomaly. Lastly, he will discuss generalizations of the 2D adjoint QCD theory that exhibit supersymmetric sectors.
 

Ian Moult
Yale University

Unveiling QCD Dynamics with Energy Correlators

Enter AbstraDetector operators, of which the average null energy operator provides the most famous example, arise as direct theoretical models of asymptotic measurements in collider experiments. It has recently become possible to directly measure correlation functions of these detector operators with extreme precision, unveiling the non-integer scaling behavior of quarks and gluons, the dynamics of QCD flux tubes, and the confinement transition.

In this talk, Ian Moult will present an overview of recent theoretical and experimental studies of these correlators, highlighting in particular their application for understanding confinement in QCD.
 

Mithat Ünsal
North Carolina State University

Self-Dual Monopole Loops, Instantons and Confinement

It is well-known that the standard instanton analysis in 4D Yang-Mills theory is plagued with the instanton size moduli problem, which renders the instanton contribution to vacuum energy density (or the one-instanton partition function) infrared divergent. The formalism also ignores the implications of the long-range (magnetic dipole type) \(1/r^4\) interaction between the small instantons, since it is weaker than a Coulomb interaction. We show that, in the \(U(1)\) lattice gauge theory, where finite action configurations are monopole loops, small loops at large separations also interact with the same type of \(1/r^4\) interaction. If one ignores the classical interactions between monopoles, following the same idea as in Yang-Mills theory, the one-monopole partition function is also infrared divergent at strong coupling. However, the \(1/r^4\) interactions among small loops should be viewed due to the multipole expansion, and they emanate from the \(1/r^2\) interaction between current segments. Taking interactions into account, one can prove that the strongly coupled \(U(1)\) lattice gauge theory is dual to a lattice abelian Higgs model, and more importantly, free of infrared divergences. The model exhibits mass gap and confinement by monopole condensation. We suggest that the structure of moduli space of instantons, ADHM data, and the long-ranged classical interactions in pure Yang-Mills theory should be examined with this refined perspective. We conjecture that, in contradistinction to the current views on the subject, internal structure of instantons in Yang-Mills theory is responsible for confinement in 4D gauge theory, similarly to the 2D sigma model.
 

Phiala Shanahan
Massachusetts Institute of Technology

Hadrons, Nuclei, and Glueballs from Lattice QCD

Phiala Shanahan will describe recent calculations that give insight into different confined states in QCD, including glueballs, hadrons, and nuclei. Shanahan will also discuss how algorithmic advances are overcoming computational limitations and progressing the state-of-the-art in this area.
 

Sergei Dubovsky
New York University

Worldsheet Axion: The Status Report
Sergei Dubovsky will review what we learned over the past few years about the properties of the only known massive excitation of the confining string — the worldsheet axion. Its properties can be studied purely theoretically, and also using lattice results and also from the real world hadron spectroscopy. After reviewing the known properties, Dubovsky will highlight the emerging puzzles and challenges which will hopefully be resolved in the near future.