The workshop will focus on exploration of physical and mathematical properties of conformal field theories (CFTs) in higher dimensions, which is a highly active area of modern mathematical physics. The talks will cover various aspects of CFTs including integrability, holography, conformal bootstrap, topological sectors and mathematical aspects. There will be only a few talks per day, leaving ample time for discussions.

Most of the talks will be at Independent University of Moscow, in central Moscow.

On 9th August the talks will be at the Skoltech Center for Advanced Study in a Moscow suburb called Skolkovo, transfer to/from IUM will be provided.

**Participation is by invitation only**

The conference is organized with the principal support of

**Interdisciplinary Scientific Center J.-V. Poncelet**

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

*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*

**Alexander Belavin** (Landau Inst. Moscow)

TBA

**Joao Caetano** (Ecole Normale Superieure Paris)

“Integrability for Non-planar N=4 SYM”

*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*

**Andrea Cavaglia** (King’s College London)

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

**Sergei Derkachev** (PDMI St-Petersburg)

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

*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*

**Anatoly Dymarsky** (Skoltech Moscow)

“Bootstrap of spinning operators in 3d”

*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*

**Alexander Gorsky** (IITP and MIPT, Moscow)

“Bands and gaps in Nekrasov partition function”

**Nikolay Gromov** (King’s College London)

TBA

**Vladimir Kazakov** (Ecole Normale Superieure Paris)

“Conformal fishnet theory”

*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*

**Vladimir Korepin** (SUNY)

“Quantum fluctuations in spin chains”

*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*

**Ivan Kostov** (CEA Saclay) and **Didina Serban** (CEA Saclay)

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

*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*

**Fedor Levkovich-Maslyuk** (Ecole Normale Superieure Paris & IITP Moscow)

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

**Yury Makeenko** (ITEP Moscow)

“Effective string beyond the Liouville action”

*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*

**Andrei Marshakov** (Skoltech, HSE Moscow)

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

**Andrei Mironov** (Lebedev Inst. Moscow)

“Correlators in tensor models and Kronecker characters”

**Enrico Olivucci** (Hamburg University)

TBA

**Andrei Onishchenko** (JINR Dubna, MIPT & MSU Moscow)

“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)

TBA

**Konstantin Zarembo** (Nordita Stockholm)

“Quantum Fluctuations of Wilson Loops”

*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*

**Alexander Zhiboedov** (Harvard)

“Analytic Euclidean Bootstrap”

*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*

10:00 – 11:30 | 11:30 – 15:30 | 15:30 – 16:30 | 16:30 – 16:50 | 16:50 – 17:50 | |||

August 6 // Monday |
Gorsky |
Lunch and discussions | Mironov |
Coffie | |||

August 7 // Tuesday | Zarembo |
Lunch and discussions | Levkovich-Maskyuk |
Coffie | Cavaglia |
||

August 8 // Wednesday | Makeenko |
Lunch and discussions | Free afternoon | ||||

August 9 // Thursday // Skoltech | Korepin11:00-12:00 |
Lunch and discussions 12:00-14:00 |
Derkachev14:00-15:00 |
Coffie 15:00-15:20 |
Alfimov15:20-16:20 |
Confe- rence dinner | |

August 10 // Friday | Zhiboedov |
Lunch and discussions | Dymarsky |
Coffie | |||

August 13 // Monday | Marshakov |
Lunch and discussions | Kazakov |
Coffie | |||

August 14 // Tuesday | Gromov |
Lunch and discussions | Olivucci |
Coffie | |||

August 15 // Wednesday | Onischenko |
Lunch and discussions | Caetano |
Coffie | |||

August 16 // Thursday | Belavin |
Lunch and discussions | Serban |
Coffie | Kostov |
Confe- rence dinner | |

August 17 // Friday | Sobko |
Lunch and discussions | |
Coffie |

We are grateful for support and assistance to

Interdisciplinary Scientific Center J.-V. Poncelet (ISCP)

Higher School of Economics (HSE)

Skoltech, Center for Advanced Studies

Independent University of Moscow

**
Please find more details in ** –

*[ last update: August 3, 2018 ]*