Mikhail Alfimov (HSE & Lebedev Inst. Moscow) [slides]

"On the applications of AdS/CFT Quantum Spectral Curve to BFKL spectrum of N=4 SYM"

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We developed a general non-perturbative framework for the BFKL spectrum of planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to study the spectrum in the whole generality, extending previously known methods to arbitrary values of conformal spin n. We show how to apply our approach to reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron dimension and get new predictions. In particular, we re-derived the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also get new non-perturbative analytic results for the Pomeron dimension in the vicinity of |n|=1, Delta=0 point and we obtained an explicit formula for the BFKL intercept function for arbitrary conformal spin up to the 3-loop order in the small coupling expansion and partial result at the 4-loop order. In addition, we implemented the numerical algorithm of arXiv:1504.06640 for non-zero conformal spin. From the numerical result we managed to deduce an analytic formula for the strong coupling expansion of the intercept function for arbitrary conformal spin.

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Vladmir Bazhanov (ANU Canberra) [slides]

"New advances in Quantum Field Theory in two-dimensions"

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Alexander Belavin (Landau Inst. Moscow) [slides]

"Special geometry on Calabi-Yau moduli spaces and Q-invariant Frobenius rings"

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Joao Caetano (Ecole Normale Superieure Paris) [slides]

“Integrability for Non-planar N=4 SYM”

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I will describe an integrability based method for the computation of correlation functions of gauge-invariant operators in N = 4 SYM theory including non-planar corrections. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test this integrability-based conjecture against a non-planar four-point correlator of half-BPS operators at one and two loops.

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Andrea Cavaglia (King's College London) [slides]

"Quantum Spectral Curve and Correlators in N=4 SYM: Part 2"

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In this talk, I will discuss the computation of the correlator of three cusps in the ladders limit in N=4 SYM, and show how the result simplifies enormously in terms of the Q functions, the key ingredients of the Quantum Spectral Curve. This strongly suggests that the latter may contain information not only on the spectrum, but also on correlation functions at finite coupling. As an outlook, I will mention some perspectives to extend the result to local operators studying the fishnet theory.

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Sergei Derkachev (PDMI St-Petersburg)

“Separation of variables for the quantum SL(3,C) spin magnet: eigenfunctions of Sklyanin B-operator"

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The quantum SL(3,C) invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of Sklyanin B-operator which define the representation of separated variables of the model.

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Anatoly Dymarsky (Skoltech Moscow) [slides]

“Bootstrap of spinning operators in 3d”

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In this talk I will review recent progress bootstrapping conserved currents and stress-energy tensors in three dimensions. The talk will include a brief introduction to the method and an outline of the main results, including the surprising necessity of light scalars in the spectrum of any 3d theories.

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Alexander Gorsky (IITP and MIPT, Moscow) [slides]

"Bands and gaps in Nekrasov partition function"

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Nikolay Gromov (King's College London)

"Exact correlators in fishnet theory"

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Vladimir Kazakov (Ecole Normale Superieure Paris) [slides]

"Conformal fishnet theory"

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I will review the construction of  four-dimensional, non-supersymmetric and  non-unitary "fishnet" CFTs, as a special double scaling limit of gamma-deformed N=4 SYM theory. Then I will describe their basic properties: regular Feynman graphs dominating the correlation functions (wheel-, spidernweb-,  brickwall-graphs etc.), the role of double-trace interactions,  the explicit integrability property in the planar limit, etc.  Computations of anomalous dimensions and OPE data for the shortest operators, via exact computations of 2-,3- and 4-point correlators, will be also reviewed.

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Vladimir Korepin (SUNY, US) [slides]

“Quantum fluctuations in spin chains”

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I will argue that the entanglement entropy measure the level of quantum fluctuations. I will consider different examples of spin chains and describe explicitly the chains with high level of fluctuations.

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Ivan Kostov (CEA Saclay) [slides] and Didina Serban (CEA Saclay) [slides]

"Taming the divergences of the three-point finction in maximally supersymmetric gauge theory - I, II”

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According to the proposal of Basso-Komatsu-Vieira, the three point function of local gauge invariant operators in N=4 SYM can be obtained by gluing two form-factor-like objects, the hexagons.
Gluing two hexagons to form a pant leg results in divergences, similar to the the infinite-volume divergences occurring in the thermodynamic Bethe Ansatz. Drawing inspiration from the form-factor program and the recent prescription by Basso, Gonçalves and Komatsu, we propose a regularisation scheme to control the multi-magnon divergences and to extract the finite part of three point function.

The first talk will introduce the basics of the hexagon proposal and the regularisation scheme.
The second talk will deal with the tree and loop expansion and the resummation of the various contributions.

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Fedor Levkovich-Maslyuk (Ecole Normale Superieure Paris & IITP Moscow) [slides]

"Quantum Spectral Curve and Correlators in N=4 SYM: Part 1"

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The Quantum Spectral Curve is a powerful framework capturing the exact spectrum of N=4 SYM. It is also expected to play a role in computing exact correlation functions via Sklyanin's separation of variables. Exploring this direction, recently with A. Cavaglia and N. Gromov we found a massive simplification of certain Wilson line correlators when recast in the QSC language. I will review the QSC construction in this context, laying the foundations for the subsequent talk of A. Cavaglia who will discuss our results for correlators. In the process I will show how the QSC captures the spectrum of special scalar insertions which has long been unreachable by integrability methods.

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Yury Makeenko (ITEP Moscow) [slides]

“Effective string beyond the Liouville action”

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I describe quantization of bosonic string about the mean-field ground state which is shown to be stable in the target-space dimension 2<d<26 contrary to the usual classical ground state which is stable  only for d<2. I compute the string susceptibility index gamma_str in the mean-field approximation and demonstrate that it differs from KPZ-DDK. I show that the total central charge equals zero in the mean-field approximation and argue that  fluctuations about the mean field do not spoil conformal invariance. Using Pauli-Villars regularization, I compute a correction to the Liouville action by going beyond the conformal anomaly and accounting for quadratic
divergences. I speculate on how the associated conformal field theory may look like.

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Andrei Marshakov (CAS Skoltech & HSE Moscow) [slides]

“Cluster integrable systems, q-deformed conformal theories and 5d Nekrasov functions”.

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Andrei Mironov (Lebedev Inst. Moscow)

"Correlators in tensor models and Kronecker characters"

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Enrico Olivucci (Hamburg University)

“Beyond 4D in Fishnet Conformal Theory and back to 2D CFT”

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The interesting features of the Integrable and Conformal fishnet field theory can be extended to any dimension via a deformation of the kinetic term. The resulting theory is non-local; nevertheless perturbative conformality holds as well as its integrability in the planar limit and conformal data for local operators can be computed exactly. The underlying quantum spin chain is SL(D,C) in complementary series representation. At D=2 the corresponding non-local CFT can be understood as an interpolation between two BFKL limits. Remarkably separation of variables for SL(2,C) chain allows the exact computation of any 4-point Basso-Dixon graphs, and points out the existence of a Matrix Model interpretation for 2D Fishnet field theory.

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Andrei Onishchenko (JINR Dubna, MIPT & MSU Moscow) [slides]

"Analytical perturbative solution of ABJM quantum spectral curve"

In this talk we are going to discuss solutions of multiloop Baxter equations arising in quantum spectral curve description of various supersymmetric quantum field theories. We will be interested in perturbative solution for anomalous dimensions of operators in sl(2) sector at arbitrary spin values. For these types of problems we propose a new method for the solution of mentioned nonhomogeneous second order difference equations directly in spectral parameter u-space for in principle arbitrary loop order. As an example we consider ABJM model and anomalous dimensions of twist 1 operators up to six loop order. The solution involves new highly nontrivial identities between hypergeometric functions, which may have various other applications. We expect this method to be generalizable to operators of other twists as well as to other theories, such as N=4 SYM.

 

Evgeny Sobko (Nordita Stockholm)

"(Super) Harmonic Analysis for (Super) Conformal Blocks"

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Konstantin Zarembo (Nordita Stockholm)

"Quantum Fluctuations of Wilson Loops”

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According to the AdS/CFT correspondence, Wilson loops couple directly to the string worldsheet. At the same time, some Wilson loop expectation values are known exactly from localization and diagram resummation, and can be confronted with explicit string-theory calculations. Going beyond the classical area law on the string side turns out extremely challenging and quantum correction had not be calculated even for the simplest Wilson loop observables until recently. I will describe how instanton calculus can be used to compute quantum corrections to Wilson loops in N=4 and N=2* theories and compared with the exact predictions of localization.

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Alexander Zhiboedov (Harvard)

"Analytic Euclidean Bootstrap"

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We will describe how to solve CFT crossing equations analytically in the deep Euclidean regime. Large scaling dimension Delta tails of the OPE spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the other channel. Subleading 1/Delta tails are systematically captured by including more operators in the Euclidean OPE in the dual channel. We use dispersion relations for conformal partial waves in the complex Delta plane, the Lorentzian inversion formula and complex tauberian theorems to derive this result.  We check our formulas in a few examples and find perfect agreement. Moreover, in these examples we observe that the large Delta expansion works very well already for small Delta~1. Finally, complex tauberian theorems are applicable to any dispersion relation and therefore could be useful for many different problems.
 

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Michelangelo Preti (ENS Paris)

"Strongly deformed N=4 SYM in the double scaling limit as an integrable CFT"

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Rob Klabbers (Hamburg University)

TBA

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