Focus Week on Quantum Mechanical Systems at Large Quantum Number




Dates: August 30 -- September 3, 2021

Venue: Online event

You can find the video recordings here.


The study of quantum mechanical systems in sectors of large quantum number leads to significant simplifications and allows the calculation of physical quantities of otherwise strongly-coupled systems in terms of an expansion in the large quantum number. Large-charge predictions have been verified to high accuracy in various independent calculations.

The topic has attracted the attention of several communities interested in conformal theories, bootstrap, superconformal theories, particle phenomenology and lattice simulations. This workshop aims to bring together people with diverse backgrounds interested in this topic.

We plan two talks by senior speakers in the mornings and contributed talks by junior participants in the afternoons, as well as time for discussion.

Invited participants and speakers:

Luis Alvarez-Gaume (Simons Center)
Philip Argyres (Cincinnati)
Shailesh Chandrasekharan (Duke)
Gabriel Cuomo (Simons SCGP/YITP Stony Brook)
Shota Komatsu (CERN)
Madalena Lemos (Durham)
Márk Mezei (Simons Center)
Eran Palti (Ben Gurion University)
Anastasios Petkou (Thessaloniki)
Diego Rodriguez-Gomez (Oviedo)
Jorge Russo (Barcelona)
Francesco Sannino (CP3 Origins)
Haruki Watanabe (Tokyo)

Organizing Committee:

Simeon Hellerman (Kavli IPMU)
Domenico Orlando (INFN Torino)
Susanne Reffert (Bern)


Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),
the University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa City, Chiba 277-8583, Japan



  • Adar Sharon
  • Ali Zahabi
  • Anastasios Petkou
  • Andrew O'Bannon
  • Diego Rodriguez-Gomez
  • Domenico Orlando
  • Eran Palti
  • Francesco Sannino
  • Gabriel Cuomo
  • Gil Badel
  • Haruki Watanabe
  • Ioannis Kalogerakis
  • Jahmall Bersini
  • Jesus Cruz Rojas
  • Jorge Russo
  • Justin Kaidi
  • Kanak Sharma
  • Luis Alvarez-Gaumé
  • Madalena Lemos
  • Mark Mezei
  • Masataka Watanabe
  • Matteo Lotito
  • Matías Torres
  • Mitch Weaver
  • Nicola Andrea Dondi
  • Ofer Aharony
  • Ohad Mamroud
  • Omar Celikbas
  • Philip Argyres
  • Rafael Moser
  • Shailesh Chandrasekharan
  • Shota Komatsu
  • Simeon Hellerman
  • Somdatta Bhattacharya
  • Sridip Pal
  • Susanne Reffert
  • Thiago Araujo
  • Thomas Chen
  • Tim Jones
  • Tim Schmidt
  • Umang Mehta
  • Vito Pellizzani
  • zafar zaman
  • 毅 庞
    • 15:30 16:30
      Charged spinning operators in the O(2) model 1h

      Large charge operators in CFTs invariant under internal symmetry can be generically associated with a superfluid phase of the theory. Therefore their correlation functions can be computed systematically within the effective field theory for the superfluid Goldstone mode. Focusing on the critical O(2) model in three dimensions, I will review this construction and extend it to include also operators with both large charge and large spin. I will discuss the results for the scaling dimension of the lightest charged operator, describing the transition from the superfluid phase to the large spin multi-trace operator regime described by the bootstrap. Based on 1711.02108 with A. de la Fuente, A. Monin, D. Pirtskhalava, R. Rattazzi and on a work in progress with Z.Komargodski.

      Speaker: Gabriel Cuomo (SCGP/YITP Stony Brook )
    • 16:30 17:30
      Conformal Dimensions in the Subleading Large Charge Sector of the O(4) model 1h
      Speaker: Shailesh Chandrasekharan (Duke University)
    • 17:30 18:00
      Operator spectrum of nonrelativistic CFTs at large charge 30m

      I will discuss the large-charge expansion of the conformal dimension Δ_Q of the lowest operator of charge Q in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an external harmonic trap that confines the particles to a spherical cloud, at the edge of which the effective theory breaks down and leads to divergences. Only recently has this issue been overcome by constructing appropriate counterterms at the edge of the cloud. I will show how to extend these results by systematically analyzing the degree of divergence of operators in the effective action and show that there always exist appropriate edge counterterms that make the final contributions to Δ_Q finite. On the other side of the correspondence, this also provides new corrections to the Thomas-Fermi approximation of the unitary Fermi gas, and I will comment on their relevance for ultracold atom physics.

      Speaker: Vito Pellizzani (University of Bern)
    • 14:30 15:30
      Large charge and higher rank N=2 SCFTs 1h
      Speaker: Philip Argyres (University of Cincinnati)
    • 15:30 16:30
      BCFT at Large Charge 1h

      We compute the spectrum of large charge operators in boundary conformal field theories (BCFTs) using the superfluid effective field theory (EFT). We verify the EFT predictions in weakly coupled examples, where computations can be done in the microscopic description. We end with a discussion of large charge phases of bulk and boundary CFTs beyond the superfluid paradigm. The talk is based on work with G. Cuomo and A. Raviv-Moshe.

      Speaker: Mark Mezei (Simons Center for Geometry and Physics, Stony Brook)
    • 17:30 18:00
      Transition of Large R-Charge Operators on a Conformal Manifold 30m

      We study a 3d N=2 supersymmetric conformal manifold using the large-charge expansion. The exactly marginal operator is shown to continuously interpolate between the "free" phase and the "superfluid" phase in the large-charge limit. We also discuss some novel aspects of the large-charge limit which appear in this model.

      Speaker: Adar Sharon (Weizmann Institute of Science)
    • 15:30 16:30
      Solving (Q)FTs via CFTs: From Weak Gravity Conjecture to Pandemics 1h
      Speaker: Francesco Sannino (Federico II University, Napoli and University of Southern Denmark)
    • 16:30 17:30
      Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture 1h

      In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we proposed a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. While we lack an understanding of why this may be true from the CFT side, it is possible to test it in simple CFTs. The conjecture passes all the tests performed so far.

      Speaker: Eran Palti (Ben Gurion University)
    • 17:30 18:00
      The O(N) model at large charge and the quartic/cubic equivalence 30m

      The large-charge expansion can be employed to find and test dualities in QFT. I illustrate this point by investigating the quartic O(N) model between four and six dimensions, where it develops a metastable UV fixed point that is believed to be equivalent to the IR fixed point of an O(N) model featuring cubic interactions. By focusing on the cubic model just below six dimensions, I show how large-charge methods allow matching an infinite series of terms between the two descriptions, reinforcing the conjectured equivalence. Next, I analyze the stability of the large-charge sector of the two models by discussing the onset of complex CFT dynamics above a critical value of the charge.

      Speaker: Jahmall Bersini (Ruđer Bošković Institute)
    • 14:00 15:00
      Bulk-boundary correspondence of topologically trivial insulators 1h

      Topological insulators are materials in which the bulk part is insulating but the surface is metallic because of protected gapless states on the surface. The correspondence between the bulk topology and the gapless surface states is called the bulk-boundary correspondence. Recently, higher-order topological insulators with gapless states localizes at hinges and corners of a crystal, rather than at surfaces, have been actively studied.

      On the other hand, it has been found that even topologically trivial insulators may also exhibit a kind of bulk-boundary correspondence. These materials are characterized by electric multipole moments in the bulk and feature fractionally quantized electric charges at hinges and corners of a crystal. In this talk, I will review these recent developments and show that, in fact, a crystal of sodium chloride (NaCl) is the simplest example of octupole insulators which have 1/8 of the elementary charge e at corners.

      Ref: HW and Hoi Chun Po, arXiv:2009.04845

      Speaker: Haruki Watanabe (The University of Tokyo)
    • 16:30 17:30
      Thermal one-point functions and single-valued polylogarithms: a spurious remark or something deeper? 1h

      I present an overview on some recent progress in thermal one-point function in CFTs for general odd dimensions. On the one hand, they can be calculated using an extension to finite temperature of analytic bootstrap techniques. On the other hand, they are associated to single-valued polylogarithms which represent multiloop amplitudes in gauge theories. Some possible implications of the latter observation will be discussed.

      Speaker: Anastasios Petkou (University of Thessaloniki)
    • 17:30 18:00
      Large quantum number expansion in O(2N) vector model and Resurgence 30m

      In this talk I will discuss the O(2N) model at criticality in three dimensions in the limit where the charge Q and N are taken to be large. The large-charge expansion turns out to be an asymptotic series and resurgent methods can be applied to obtain an unambiguous semi-classical reconstruction of this expansion. It contains non-perturbative corrections and it allows to extend the validity of the EFT to any value of the charge. Otherwise, this reconstruction can be emanated from a saddle point expansion of worldline path integrals for free particles moving on spheres.

      Speaker: Ioannis Kalogerakis (University of Bern)
    • 15:30 16:30
      Comments on Large Charge and Holography 1h

      I will discuss three topics on the large charge limit and holography. First, I will discuss general features of the large-charge limit of superconformal field theories at large N. In particular, I will point out a simple setup to analyze the large charge expansion of the planar N=4 super Yang-Mills and discuss its holographic interpretation. Second, I will point out the hidden symmetry of the double-scaling limit of N=4 super Yang-Mills at large charge. Third I will discuss the large-charge limit of the defect CFT on the Wilson line and its relation to the matrix model.

      Speaker: Shota Komatsu (CERN)
    • 16:30 17:30
      Regge trajectories for N=(2,0) superconformal field theories 1h

      We discuss the structure of Regge trajectories of 6d N=(2,0) SCFTs combining analyticity in spin with supersymmetry. Focusing on the four-point function of supermultiplet we show how "analyticity in spin" holds for all spins greater than -3. Through the Lorentzian inversion formula we then describe an iterative procedure to "bootstrap" this four-point function starting from protected data, and compare the results with the numerical bootstrap bounds. This procedure works best at large but finite central charge, where non-protected contributions are suppressed by the inversion formula.

      Speaker: Madalena Lemos (Durham University)
    • 17:30 18:00
      The large charge sector of 3d parity-violating CFTs 30m

      For CFTs that become superfluids at finite density, we show that there exists a single one-derivative term in the Goldstone EFT that has a quantized coefficient. This term requires the ground state on a sphere to have vortices, and results in a spectrum of operators that is remarkably different from CFTs that are parity invariant. We will show how the properties predicted by the Goldstone EFT are realized in the spectrum of monopole operators in a weakly coupled Chern-Simons matter theory. Based on arxiv:2102.05046 with Luca Delacretaz and Gabriel Cuomo.

      Speaker: Umang Mehta (Kadanoff Center for Theoretical Physics, University of Chicago)