From 26 to 31 August 2019, a regular International Workshop “Supersymmetries and Quantum Symmetries” (SQS’19) was held in Yerevan. It was organized by the Bogoliubov Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research and the Yerevan Physical Institute.

Workshops “Supersymmetry and Quantum Symmetries” (SQS) have been held in the Laboratory of Theoretical Physics since 1989 on the initiative of Victor Isaakovich Ogievetsky (1928 – 1996). In 1993, the Workshop gained international status. Since 1996, following the death of Viktor Isaakovich, SQS meetings have been held every two years in commemoration of an outstanding contribution of this remarkable scientist in theoretical physics. Topics of the Workshop traditionally include the areas of research that were especially interesting for V.I. Ogievetsky, including string theory, quantum groups, grand unified theory, integrated systems, etc. This set of issues remains the focus of attention for all involved in modern theoretical high-energy physics and mathematical physics.

The SQS meeting took place in Yerevan for the first time. It was the second time the Workshop was organized not in Dubna (SQS’01 was held in Karpacz not far from Wroclaw, Poland). Yerevan was chosen because of many years of close cooperation between Armenian theoreticians and colleagues from Dubna and because many of them are world-recognised experts in the fields the programme of the Workshop covers. The Workshop held in the capital city of Armenia, a JINR Member State, was aimed to strengthen scientific contacts of Armenian scientists with their Russian colleagues from Dubna, Moscow, Tomsk, and other regions, as well as to establish new contacts of scientists from Armenia and neighbouring countries with leading theoreticians from Russia and JINR. Another significant reason to hold SQS’19 in Armenia was that the founder of the SQS series V. I. Ogievetsky regularly visited Yerevan and had many friends among Armenian scientists.

The previous meeting of the SQS series took place in summer 2017 in Dubna. New fascinating results have been achieved since then that have become the object of scientific reports and discussions at SQS’19. Although supersymmetry has not been yet experimentally discovered (active search for superpartners of famous particles are being conducted in numerous scientific centres, including the supercollider in CERN), its attractive concept as a symmetry between bosons and fermions is the basis for modern theories aimed to provide general description of interactions (superstrings, higher spin theories, etc.). Particularly this type of supersymmetry guarantees the self-coherence of the mentioned theories and has already allowed overcoming numerous pitfalls that have been faced while formulating them. That is why most theoreticians have no doubts that later or sooner supersymmetry will be experimentally proven just like other fundamental natural symmetries. Nowadays, the process of further development of the concept of supersymmetry and a deeper understanding of its role in the description of the micro-world physics is underway. The SQS meetings greatly help in systematization of these studies and the exchange of new ideas. That is the major reason for a considerable interest in them among world-leading specialists in the fields of symmetries and relevant issues of the quantum field theory.

Like in previous years, the SQS’19 meeting was meaningful and fruitful. It was attended by more than 100 scientists from Australia, Armenia, Belgium, Brazil, Bulgaria, the Czech Republic, Chile, Croatia, Cyprus, France, Georgia, Germany, Great Britain, Greece, Iran, Ireland, Italy, Japan, the Republic of Korea, Netherlands, Poland, Russia, Spain, Sweden, Thailand, Turkey, and the USA. Among them, there were Gleb Arutyunov (Hamburg), Igor Bandos (Bilbao), Glenn Barnich (Bruxelles), Mikhail Vasiliev (LPI), Bernard de Wit (Utrecht), Jerzy Lukierski (Wroclaw), Sergey Kuzenko (Perth), Nikolas Boulanger (Mons), Olaf Lechtenfeld (Hannover), Ruben Minasian (Saclay), Martin Cederwall (Göteborg), and many other leading scientists in the fields of particle theory, supersymmetric quantum field theory, gravitation and the string theory, noncommutative geometry, and the theory of integrated systems.

The SQS meetings have been always marked for their high level of involvement of young talented researchers from Russia and the neighbouring countries as well, and it has contributed to the strengthening and development of traditions of the Russian (and Soviet) school of theoretical physics and their maintenance. This year, there were many young participants from Russia, Armenia, Iran, and Turkey as well as the scientific youth from theoretical centres of other countries. It should be mentioned that the International Centre for Theoretical Physics (ICTP) supported the participation of young scientists from the Middle Eastern countries. Many young theoreticians took part in the event of such level for the first time.

93 reports were presented at the SQS’19, 26 of which were plenary, 57 of them were sectional and 10 poster reports. They covered the following topics:

• Theories of superstrings and higher spins;
• Quantum and geometric aspects of supersymmetry theories;
• Integrable models and their superextensions;
• Quantum groups and noncommutative geometry;
• Standard model, gravitation and cosmology.

These issues are at the front edge of research in theoretical and mathematical physics. They are related to the concept of supersymmetry to a certain extent, and any advancement in their study allows getting closer to a better understanding of physical phenomena at both levels, microworld and space. In particular, the study of supersymmetric models of quantum field theory in various dimensions as well as theories of higher spins may provide valuable information about the structure of the fundamental theory, which “lives”, according to existing opinions, in the 11-dimensional space-time and includes the string theory. Such research encourages the development of new physical-theoretical and mathematical methods that may be used in related scientific fields.

Please, find below a short overview of major results reported at the meeting.

Theories of superstrings and higher spin fields were among the major topics of the meeting. For the last several years, the link between the higher spin theory and the superstring theory became clear. So, many reports were made on the link between these two fundamental theories.

Mikhail Vasiliev (Moscow) in his report told about the relation between the higher spin theory and the superstring theory and made an overview of recent results. The displaced homotopic scheme was proposed, which leads to spin-local heights of higher spins obtained in non-linear equations. A more detailed discussion of the latter issue with particular examples was the object of reports by Olga Gelfond and Vyacheslav Didenko.

Alexey Isaev (Dubna) told about a new twistorial description of massless infinite spin. Relevant N=1 supermultiplets with the infinite (continuous) spin were derived.

The report by E. Skvortsov (Munich) considered the problems of quantization of gravity using higher spin fields.

The report by Ruben Minasian (Saklay) was devoted to anomalies in various superstring theories.

The reports on quantum and geometric aspects of supersymmetric (and non-supersymmetric) theories considered both many-dimensional supersymmetric models and one-dimensional systems that allow conducting quantum and mechanical analysis of the theories of this type.

Igor Bandos (Bilbao) in his report studied supermembranes and domain walls in D=4 supersymmetric theories. He presented the results that may be useful for determining effective actions of phenomenologically interesting models of the string theory compactification with open branes and branes at the boundaries of open branes. Sergey Kuzenko (Perth) told about generalized Fayet–Iliopoulos terms in supergravity studied for the last two years, which do not demand calibrated R-symmetry. At the conclusion of his report, he said that generalized Fayet–Iliopoulos terms could be also produced quantum-mechanically. The report by Ilya Bakhmatov (Pohang) was devoted to generalized Yang–Baxter deformations in the 11-dimensional supergravity.

Integrable models, quantum groups and noncommutative geometry were the topics of numerous reports.

Vladimir Sokolov (Chernogolovka) in his report concluding the meeting told about integrated non-linear differential equations with matrix variables. The main peculiarity of the considered integrable systems is the existence of small polynomial symmetries and first integrals in them.

The report by Gleb Arutyunov (Hamburg) considered the hyperbolic spin Ruijsenaars-Schneider many-body model with spin degrees of freedom. He showed that the obtained model is superintegrable.

Anna Pachol (London) in her report introduced to the noncommutative digital differential geometry which studies the quantum Riemannian geometry over the fields of two elements 0 and 1. This technique is used to study quantum gravity and allows considering geometric backgrounds using discrete approximation such as a grid or graphs. Thus, these systems are better calculated.

The reports on the standard model, gravity theory and cosmology considered both modern experimental data on particles and topical cosmological results and problems.

Burt Ovrut (Philadelphia, the USA) in his report told about the R-parity violating decays of Wino Chargino and Wino Neutralino, the lightest supersymmetric particles, in the B-L MSSM.

Glenn Barnich (Brussels) reported on thermodynamics of charged vacuum condensate as a physical model for the gravity task using the method developed by Gibbons and Hawking.

Several reports referred mainly to mathematics, for example, the reports by Arthemy Kiselev (Gröningen), Alexander Elashvili (Tbilisi), Oleg Ogievetsky (Marcel) and Todor Popov (Sofia). We had to leave their and many other interesting reports “off-screen” due to the limits imposed on the volume of the article. Proceedings of the SQS’19 will be published in 2020, and most of the reports are already available on the website.

Results of the meeting highlighted one more time the crucial role of supersymmetry and quantum symmetries in a challenging problem of developing the future joint theory of all interactions as well as fruitful international cooperation, in particular, on the platform of the Joint Institute for Nuclear Research. Many of the presented reports were based on such international cooperation, including cooperation between BLTP and YePI. Participants of the meeting discussed plans for further joint projects. Most of the participants are going to take part in the following meeting, SQS’21.

The organizing committee of the SQS’19 meeting expresses its gratitude to the staff of the Laboratory of Theoretical Physics JINR and the Yerevan Physical Institute for invaluable aid in organization of the conference that in many terms contributed to its success. The meeting would not happen without the financial support of the Laboratory of Theoretical Physics JINR, the Science Committee of the Republic of Armenia, the Volkswagen Foundation and the International Centre for Theoretical Physics in Trieste. SQS’19 organizers express their sincere gratitude to all sponsors of the meeting.

Evgeny Ivanov, Chairman of the SQS’19 organizing committee
Armen Nersessian, Co-Chairman of the SQS’19 organizing committee
Stepan Sidorov, SQS’19 Scientific Secretary
Photos by Mesrop Oganessian