Integrability, Anomalies and Quantum Field Theory

10 févr. 2020, 09:00 → 14 févr. 2020, 18:00 Europe/Paris

Marilyn and James Simons Conference Center (IHES)

 A conference in honor of Samson Shatashvili's 60th birthday

The interactions of Mathematics and Physics have greatly intensified during the last three decades, and it led to a number of very significant breakthroughs in Mathematics. Among other things, these breakthroughs include new invariants of 3 and 4-dimensional manifolds, the discovery of mirror symmetry in Algebraic Geometry, and the theory of deformation quantization. This progress became possible due to close interactions between Mathematics and theoretical Physics and due to the dialogue between mathematicians and physicists working on similar problems but using very different methods.

The conference will touch upon two important aspects of interaction between Mathematics and Quantum Field Theory: Quantum Integrability and Anomalies. It will honour Professor Samson Shatashvili on the occasion of his 60th birthday.

Professor Samson Shatashvili made deep contributions in the theory of anomalies and in quantum integrability. In particular, in collaboration with L. Faddeev he discovered the interpretation of gauge theory anomalies in terms of abelian extensions of gauge groups on manifolds of odd dimension. In the theory of quantum integrability, together with a number of collaborators he discovered a deep link between Bethe equations and supersymmetric quantum gauge theory. Professor Shatashvili (of the Trinity College, Dublin and the Simons Center for Geometry and Physics, Stony Brook) served as a Louis Michel Chair and then as an Israel Gelfand Chair at IHES for many years. He contributed in a significant way in the development of ideas and in the unique research atmosphere of IHES.

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Organisers: Anton Alekseev (Université de Genève) & Maxim Kontsevich (IHES)

Invited speakers include:

• Costas Bachas (ENS-Paris)
• Jean-Michel Bismut (Université Paris-Sud Orsay)
• Gregory Gabadadze (New York University)
• Sergei Gukov (Caltech)
• Simeon Hellerman (IPMU)
• Chris Hull (Imperial College London)
• Vladimir Kazakov (ENS-Paris)
• Zohar Komargodski (SCGP)
• Vladimir Korepin (Stony Brook University)
• Manuela Kulaxizi (Trinity College Dublin)
• Sergei Lukyanov (Rutgers University)
• Ruben Minasian (IPhT - CEA Saclay)
• Vasily Pestun (IHES)
• Alexey Rosly (ITEP, Skoltech, HSE, IITP, Moscow)
• Sinead Ryan (Trinity College Dublin)
• Ivo Sachs (LMU Munich)
• Nana Shatashvili (Tbilisi State University, Georgia)
• Fedor Smirnov (LPTHE Sorbonne-Université)
• Leon Takhtajan (Stony Brook University)
• Anne Taormina (Durham University)
• Cumrum Vafa (Harvard University)
• Pierre Vanhove (IPhT & CEA Saclay)
• Erik Verlinde (Universiteit van Amsterdam)
• Alexander Zamolodchikov (Stony Brook University)

 

Avec le soutien du LHM

PLAYLIST VIDEOS

lundi 10 février

09:00 Registration of the participants and Welcome coffee

1 Supersymmetric Quantum Field Theories and the Swampland

Orateur: Prof. Cumrun VAFA (Harvard University)

VIDEO

11:00 Coffee break

2 Anomalies, Inflow and Holography

I will review the M5 anomalies in M-theory and their cancellation mechanism, and discuss its implications for the lower-dimensional super conformal field theories.

Orateur: Prof. Ruben MINASIAN (IPhT - CEA Saclay)

VIDEO

12:30 Lunch break

3 Conformal Properties of the Self-Dual YM Theory

I would like to promote the Self-Dual Yang Mills Theory as a possibly simplest non-linear conformal field theory in 4d with no supersymmetry. This field theory possesses UV divergences, but these do not spoil the conformal covariance: the effect of renormalization is that the coupling constant does not run, it is only a field renormalization which is needed. This results in a conformal invariance of the effective action under anomalous conformal transformations. I can give only a partial, but hopefully convincing proof of the latter. If the time permits I will also discuss the issue of conformal observables in this theory in relation with twistor geometry.

Orateur: Prof. Alexey ROSLY (ITEP, Skoltech, HSE, IITP, Moscow)

VIDEO

4 Diagonal Matrix Elements for the Sinh-Gordon Model in Finite Volume

Sinh-Gordon model is the simplest integrable model of QFT which is interesting, in particular, due to its relation to the Liouville model. In this talk I shall present hypothetical formulae for the diagonal matrix elements. The stress will be put on the UV limit and its relation to the Liouville three points functions.

Orateur: Prof. Fedor SMIRNOV (LPTHE - Sorbonne Université)

VIDEO

16:00 Coffee break

5 Conformal Fishnet Theory

I will review the properties and recent results for conformal fishnet theory (FCFT) which was proposed by O. Gurdogan and myself as a special double scaling limit of gamma-twisted N=4 SYM theory. FCFT, in its simplest, bi-scalar version, is a UV finite strongly coupled 4-dimensional logarithmic CFT dominated by planar fishnet Feynman graphs (of the shape of regular square lattice). FCFT inherits the planar integrability of N=4 SYM which becomes manifest in this case: the fishnet graphs can be mapped on the SO(2,4) integrable spin chain (A. Zamolodchikov, 1980). The D-dimensional generalization of FCFT, with SO(2,D) conformal symmetry can be also provided. A remarkable property of FCFT is the possibility of spontaneous symmetry breaking, which is not lifted by quantum corrections. I will also discuss the exact computation of certain anomalous dimensions and 4-point correlators, and of related fishnet Feynman graphs (of "wheel" or "spiral" type), using the quantum integrability tools: asymptotic and thermodynamic Bethe ansatz and quantum spectral curve.

Orateur: Prof. Vladimir KAZAKOV (ENS-Paris)

VIDEO

mardi 11 février

09:30 Welcome coffee

6 Degeneration, Geometry and Duality

Orateur: Prof. Chris HULL (Imperial College London)

VIDEO

11:00 Coffee break

7 Mathieu Moonshine: Symmetry Surfing and Quarter BPS States at the Kummer Point

The elliptic genus of K3 surfaces encrypts an intriguing connection between the sporadic group Mathieu 24 and non-linear sigma models on K3, dubbed “Mathieu Moonshine”. By restricting to Kummer K3 surfaces, which may be constructed as Z2 orbifolds of complex 2-tori with blown up singularities, it has been possible to devise a framework in which the concept of symmetry surfing can be explored and tested in a concrete way. This talk focusses on what has been learned so far that supports the symmetry surfing idea when lifting the Kummer construction to the level of conformal field theory, with particular emphasis on quarter BPS states. Some of these states enter the elliptic genus with opposite signs thus cancelling each other when counted by this index, yet they carry interesting information that should help understand Mathieu Moonshine.

Orateur: Prof. Anne TAORMINA (Durham University)

VIDEO

12:30 Lunch break

8 Fokker-Planck Operators and the Center of the Enveloping Algebra

The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals.
Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the Casimir operator of a reductive group, this computation being related to Selberg's trace formula. The analogue of the heat equation method is now a suitable deformation of the Laplacian by a family of Fokker-Planck operators. In joint work with Shu SHEN, we have also shown how to extend these formulas to orbital integrals involving general elements of the center of the enveloping algebra.

Orateur: Prof. Jean-Michel BISMUT (Université Paris-Sud Orsay)

VIDEO

9 Integrability, Theory Space, and My Debt To Samson Shatashvili

Orateur: Prof. Simeon HELLERMAN (IPMU)

VIDEO

16:00 Coffee break

10 Generalized Beltrami-Bernoulli Flow Model for Astrophysical Disk-Jet Structure Formation

In the vicinity of a massive object of various scales (ranging from young stars to galactic nuclei), mass flow creates a spectacular structure combining a thin disk and collimated jet. Despite a wide range of scaling parameters, they exhibit a remarkable similarity that must be dictated by a universal principle. A generalized Beltrami condition has been formulated as a succinct representation of such a principle. The singularity at the center of the Keplerian rotation forces the flow to align with the “generalized vorticity” (including the effect of localized density and finite dissipation) which appears as an axle penetrating the disk – hence, the collimated jet is a Beltrami flow. An analytical expression of a disk-jet system has been constructed. Employing the Beltrami-Bernoulli flow configuration of disk-jet structure we apply our model for the analytic description of hydrodynamic jets from protostellar disks. For this purpose, we extend the standard turbulent viscosity prescription and derive several classes of analytic solutions using the flow parametrization in self-similar variables. Derived solutions describe the disk-jet structure, where, for the first time, jet properties are analytically linked with the properties of the accretion disk flow. These solutions can be used to analyze the astrophysical jets from protostellar accretion disks and link the properties of outflows with the local observational properties of accretion disk flows.

Orateur: Prof. Nana SHATASHVILI (Tbilisi State University, Georgia)

VIDEO

mercredi 12 février

09:30 Welcome coffee

11 Title to be confirmed

Orateur: Prof. Erik VERLINDE (Univerteit van Amsterdam)

VIDEO

11:00 Coffee break

12 Coupling Holographic Universes

I will discuss some recent progress on interacting-graviton theories in the context of the AdS/CFT correspondence.

Orateur: Prof. Costas BACHAS (ENS-Paris)

VIDEO

12:30 Lunch break

13 New Results and Applications

I will review the concept of anomalies and its relationship with Symmetry Protected Topological Phases. I will also review various extensions of the concept of ‘’symmetry.’’ I will present applications to Yang-Mills theories in 2, 3 and 4 dimensions. These applications feature two extensions of the concept of symmetry: one is higher-symmetry and the other is "non-symmetry" topological defects.

Orateur: Prof. Zohar KOMARGODSKI (SCGP)

VIDEO

14 CFT and Black Holes

We will review progress in studying CFTs with a large number of degrees of freedom, and discuss how we can use it to learn something about gravity and black holes.

Orateur: Prof. Manuela KULAXIZI (Trinity College Dublin)

VIDEO

16:00 Coffee break

15 Space Time Actions from The World Line

I will describe how the full non-linear equations of motion for all massless NS-sector fields of the string arise from world line quantization of the spinning particle. Somewhat surprisingly this includes the dilation which is often thought to be stringy in nature.

Orateur: Prof. Ivo SACHS (MLU Munich)

VIDEO

jeudi 13 février

09:30 Welcome coffee

16 Integrable QM Operators from Mirror Curves

Orateur: Prof. Leon TAKHTAJAN (Stony Brook University)

VIDEO

11:00 Coffee break

17 Reflection Operators in Integrable CFT

The reflection operators are one of the simplest examples of the non-local integrals of motion in an integrable 2D CFT. They have many interesting applications, including for the description of the UV behavior of massive integrable perturbations of the CFT. In this talk, we’ll discuss the reflection operator in the context of the integrable structure that appears in the study of the quantum KdV theory. This operator is closely related to the Liouville reflection S-matrix. Briefly mentioned will be a new result concerning the full spectrum of this reflection operator, which was obtained recently within the framework of the ODE/IQFT correspondence.

Orateur: Prof. Sergei LUKYANOV (Rutgers University)

VIDEO

12:30 Lunch break

18 Field Theory for Massive Gravity and Cosmology

I will review the status of the theory of massive gravity, and will briefly discuss its applications in cosmology.

Orateur: Prof. Gregory GABADADZE (New York University)

VIDEO

19 QCD: Numerical Integration of a Quantum Field Theory

At hadronic energy scales, quantum chromodynamics (QCD) requires a nonperturbative treatment to calculate physical observables. Lattice QCD is a nonperturbative framework that facilitates numerical simulation of the theory and is the only known systematically-improvable approach to calculate phenomenological relevant QCD parameters. I will discuss the lattice as a regulator for QCD, describe the current state-of-the-art and offer some perspectives for future directions.

Orateur: Prof. Sinéad RYAN (Trinity College Dublin)

VIDEO

16:00 Coffee break

20 New Dualities from Anomalies, and New Anomalies from Dualities

Orateur: Prof. Sergei GUKOV (Caltech)

VIDEO

vendredi 14 février

09:30 Welcome coffee

21 Lattice Nonlinear Schroedinger Equation

Orateur: Prof. Vladimir KOREPIN (Stony Brook University)

VIDEO

11:00 Coffee break

22 Mirror Symmetry and Feynman Integrals

Orateur: Prof. Pierre VANHOVE (IPhT - CEA Saclay)

VIDEO

12:30 Lunch break

23 Multiplicative Higgs Bundles

In this talk we'll establish the symplectic isomorphism between symplectic varieties obtained as (i) the symplectic leaves in the rational Poisson Lie group equipped with Sklyanin's Poisson structure, (ii) the moduli space of multiplicative Higgs bundles on P1 and (iii) the moduli space of periodic monopoles on R2xS1.

Orateur: Prof. Vasily PESTUN (IHES)

VIDEO