# Conformal field theories in higher dimensions 2020

Exploration of conformal field theories (CFTs) is one of the key areas in modern theoretical physics where progress is happening at a rapid pace. The workshop will cover various aspects of CFTs as well as related topics, focusing in particular on higher-dimensional cases such as 3d and 4d theories. Areas discussed will include integrability, holography, conformal bootstrap and mathematical aspects.

Organizing committee:

Vladimir Kazakov, chair (ENS Paris)

Mikhail Alfimov (HSE & Lebedev Inst.)

Nikolay Gromov (King's College London)

Fedor Levkovich-Maslyuk (ENS Paris & IITP Moscow)

Konstantin Zarembo (Nordita Inst., Stockholm)

Program Committee:

Nikolay Gromov, deputy chair

Konstantin Zarembo, chair

Titles and abstracts

Nadav Drukker (King's College London)

Surface operators in the 6d N=(2,0) theory

I will discuss the anomalies of surface operator observables in 6d. I will review some of the background and past calculations, will present some generalizations and finally some new results employing contemporary techniques in theoretical physics.

Victor Gorbenko (IAS Princeton)

On Complex CFTs

Ben Hoare (ETH Zurich)

Yang-Baxter deformations with Drinfel'd-Jimbo R-matrices

The Yang-Baxter deformation is a systematic way to deform integrable sigma models. When the deformation is governed by a Drinfel'd-Jimbo R-matrix the global symmetry of the model is q-deformed. We will review recent developments in the study of these models, including the q-deformation of the AdS5 x S5 superstring, with the goal of exploring how the choice of R-matrix affects the physics.

Charlotte Kristjansen (NBI Copenhagen)

One-point functions in AdS/dCFT with and without supersymmetry

We review recent results on the calculation of one-point functions in dCFTs corresponding to N=4 SYM with domain walls, discussing supersymmetric as well as non-supersymmetric cases. In particular, we address the integrability properties of the theories and the status of the comparison to dual string theoretical computations.

Michelangelo Preti (Nordita Stockholm)

Integrable fishnets and exact four-point functions from N=2 quivers

We propose the γ-deformation of four-dimensional N = 2 quiver gauge theories, obtained by applying the Lunin-Maldacena deformation with respect to the U(1)×SU(2) R-symmetry. The resulting theory is supplied with double-trace counterterms and has a non-trivial RG-flow. We compute the one-loop β-function and identify the conformal fixed points of these theories. Furthermore, we study the double-scaling limit of large imaginary γ and weak ’t Hooft coupling. In this regime, both gauge fields and hypermultiplets decouple, leaving a non-supersymmetric, non-gauge theory where gluinos and vector multiplet scalars interact via Yukawa couplings. This model is integrable even though the original N = 2 theory is not. Indeed, the anomalous dimension of the BMN vacuum is dominated by fermionic wheel graphs, whose bulk constitutes an integrable fishnet. We compute this scaling dimension to leading order directly from Feynman diagrams both for the general γ-deformation and the double-scaled theory. Finally we study certain four-point functions summing up exactly the corresponding Feynman diagrams by Bethe-Salpeter method. This provides explicit OPE data for various operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.

Alexei Rosly (ITEP, Skoltech, HSE Moscow)

Conformal properties of the Self-Dual YM Theory

Larus Thorlacius (Stockholm U. & Iceland U.)

Semi-classical black hole complexity

We obtain the holographic complexity of an evaporating black hole in

the semi-classical RST model. The complexity of the combined system

of black hole and outgoing Hawking radiation monotonically grows during

the evaporation process but the rate of complexity growth decreases as

the black hole shrinks. At any given time, the growth rate is proportional

to the area of the stretched horizon of the evaporating black hole.

**Submitted by NataliaNatalia |

**13 / Mar / 2020