Download Modern Mathematical Physics

Modern Mathematical Physics:
gravity, supersymmetry and integrability
Report for 2003-2007 (theme 1047)
Scientific leader: A.T.Filippov
Leaders: A.S.Sorin, A.P.Isaev
Programme Advisory Committee for Particle Physics
29 meeting, June 10-11 2008
MATHEMATICAL PHYSICS
IS
“KNOW-HOW”
IN THEORETICAL PHYSICS
Modern Mathematical Physics
(projects)
• Quantum Groups and Integrable
Systems
Leaders: A.P.Isaev, A.A.Vladimirov
• Supersymmetry
Leader: E.A.Ivanov
• Gravity, Cosmology and Strings
Leaders: A.T.Filippov, V.V.Nesterenko, A.S.Sorin
I
Isaev А.P.
Burdik C.
Мir-Каsimov R.М.
Мitryushkin V.К.
Оs’kin А.F.
Pakuliak S.Z.
Pogosyan G.S.
Sissakian A.N.
Тyurin N.А.
II
Ivanov Е.А.
Zupnik B.М.
Кrivonos S.О.
Sirilo D.H.
Sutulin А.О.
Fedoruk S.А.
Pentek M.
Doctor of science – 15
PhD
– 11
Without degree
–7+2
(including - 1 postdocs,
1 PhD student, 4 students,
1 postgraduate)
___________________
Total: 33 + 2
Arnaeva А.
Belev S.
III
Filippov A.T.
Nesterenko V.V.
Sorin A.S.
Barbashov B.M.
Dimitrov B.
Ivanova T.A.
Tret’yakov P.V.
Pestov A.B.
Pirozhenko I.G.
Popov A.D.
Tagirov E.A.
Fursaev D.V.
Shavokhina N.
Taniyldyzy Sh.F.
Egorova I.А.
Кozlovsky S.А.
Теlezhnikov S.
Basic directions for investigations
I. Quantum groups and integrable systems
II. Supersymmetry
III. Gravity, cosmology and (super)strings
Вasic results
Investigations were performed in the
following directions:
supergravity and superstring theories
development of the methods of modern mathematical
physics and their application to the fundamental
problems of theoretical physics
study of the new types of (super)symmetries
In the framework of integrable gravity models the
physics of black holes was investigated and the
relationship was discovered between the static states,
cosmological scenarios, and wave-like solutions.
A.T.Filippov, “A New Integrable Model of (1+1)-Dimensional
Dilaton Gravity Coupled to Toda Matter”, arXiv:0801.1312;
"Integrable Models of 1+1 Dimensional Dilaton Gravity
Coupled to Scalar Matter", Theor. Math. Phys. 146 (2006) 95107; "Dimensional Reduction of Gravity and Relation between
Static States, Cosmologies and Waves",hep-th/0612258.
The properties of entanglement entropy, generated by
the spatial separation of fundamental degrees
of freedom, were investigated. The results can be used
for elucidating the microscopic origin of the BekensteinHawking entropy in the black hole physics.
D.V.Fursaev, “Entanglement entropy in quantum gravity and
the Plateau groblem, arXiv:0711.1221
Cosmic billiard
Cosmic evolution can be seen as a smooth billiard scattering
with quantized angles defined by the Weyl group of the
U-duality of supersting theory
Pietro Fre and Alexander Sorin
Nucl.Phys. B733 (2006) 334,
arXiv:0710.1059 (2007)
FUTUR
E
UNIVERSE EVOLUTION:
 Smooth Weyl reflections
 Dynamical hyperplanes
Billiard table  Weyl chamber
Time arrow  Weyl group ordering
(entropy)
Bounces
Walls
PAST
Integrable open (spin) chain models of gl(n|m)- and osp(n|m)-type
were formulated in algebraic terms. It helps to investigate these
models (which generalize Heisenberg spin chains) from unified
point of view. In particular the energy spectrum for these spin
chains were explicitly found in special cases of chains.
These investigations are important in statistical
mechanics and (as it was shown recently) in (super)
Yang-Mills field theories. E.g.,
energy spectrum for special spin chains =
= anomaly dimensions in QCD for high energies !!!
A.P. Isaev and O.V. Ogievetsky, "On Baxterized Solutions of Reflection
Equation and Integrable Chain Models",
Nucl. Phys. B 760 [PM] (2007) 167-183;
A.P. Isaev, O.V. Ogievetsky and A.F. Os'kin, "Chain models on Hecke
algebra for corner type representations",
Rep. on Math. Phys. 61, No.2 (2008) 309 – 315.
Once again about spin chain models:
The projection method for constructing the states of
quantum integrable models was formulated and
compared to the nested Bethe ansatz. Universal Bethe
equations were obtained allowing to unify hierarchical
and analytical Bethe ansatzes in one frame. This theory
describes the universal properties of the space of states
in the quantum integrable models associated with the
algebras gl(N).
B. Enriquez, S. Khoroshkin, S. Pakuliak,
``Weight functions and Drinfeld currents``,
Comm. Math. Phys. 276 (2007) 691-725
The generalization of the BRST approach to the
quantization of models with quadratic constraints was
developed. The method gives the possibility to describe
the whole spectrum of massive and massless higher
spin fields including the models on the curved anti-de
Sitter spaces.
X. Bekaert, I.L. Buchbinder, A. Pashnev, M. Tsulaia,”On higher
spin theory: Strings, BRST, dimensional reductions'',
Class. Quant. Grav. 21 (2004) S1457-1464.
A.P. Isaev and O.V. Ogievetsky,
"BRST Operator for Quantum Lie Algebras: Explicit Formula",
Int. J. Mod. Phys. A., Vol. 19, Supplement (2004) 240-247.
Fermion
Boson
Fermion
Boson
Theories
with
deformed
supersymmetry
were
investigated. Theories with the “nonanticommutative”
deformations were constructed and analysed in the case
of extended (N=2 and N=4) supersymmetry in four
dimensions. Such deformations can be treated as an
alternative mechanism of supersymmetry breaking.
E. Ivanov, O. Lechtenfeld, B. Zupnik,
``Nilpotent deformations of N=2 superspace'',JHEP
0402 (2004) 012.
S. Ferrara, E. Ivanov, O. Lechtenfeld, E. Sokatchev,
B. Zupnik,``Non-anticommutative chiral singlet
deformation of N=(1,1) gauge theory'',Nucl. Phys. B
704 (2005) 154-180
The properties of supersymmetric field theopries in
diverse dimensions were studied on the basis of
supersymmetric quantum mechanics. Some of these
models are the supersymmetric extensions of some
important integrable one-dimensional systems
(Calogero-Moser models, various versions of the
Landau problem, etc). A new class of mechanics
models with extended N=4 and N=8 supersymmetries
was proposed and studied.
S. Bellucci, E. Ivanov, S. Krivonos, O. Lechtenfeld,``ABC of
N = 8, D = 1 supermultiplets'',Nucl. Phys. B 699 (2004) 226252
E. Ivanov, O. Lechtenfeld, A. Sutulin,``Hierarchy of N=8
Mechanics Models'', Nucl. Phys. B 790 (2008) 493-523
Lagrangian tori for the projective plane and other toric
Fano varieties were studied in the context of the
Mirror Symmetry Conjecture for Fano varieties given
by Hori and Vafa. The Hori - Vafa conjecture can be
formulated in terms of the Bohr - Sommerfeld
conditions, which implies a relationship between
Mirror Symmetry and Geometric Quantization in
terms of Lagrangian geometry.
N.A.Tyurin, “Geometric quantization in algebraic
Lagrangian geometry”, London Mathematical
Society, Lecture Notes 338 (2007)
Publications
Моnographs
– 2
1.) A.Galperin, E.Ivanov, V.Ogievetsky, E.Sokatchev “Harminic Superspace”,
Cambrige University Press (2007), Second Edition
2.) N.A.Tyurin, “Geometric quantization in algebraic lagrangian geometry”,
London Mathematical Society, Lecture Notes 338 (2007)
Journals
~ 210
Conference contributions ~ 60
_____________________________________
Total ~ 272
Published in:
Nucl. Phys. B
Phys.Rev. A
Phys. Lett. B
Lett.Math.Phys.
JHEP
Mod.Phys.Lett.
Phys. Rev. D
Russian Math. Surveys
Тheor.Мat.Phys.
Algebra and Analysis
Comm.Math.Phys.
Int.Journ.Math.Phys.
Class.Quant.Grav.
J.Math.Phys.
J.Phys. A
J.Geom.Phys.
Found.Phys.
Contemp.Math.
Amer.Math.Soc.
London Math.Soc.
Yadernaya Fizika
Phys.Elem.Part. & Atom.Nucl.
Letters in PEPAN
Europhys.Lett.
International collaboration
Reports at conferences and lectures at schools
~ 130
Collaboration visits ~ 70
Visitors to BLTP
~ 60
Countries:
JINR Member States, CERN, Australia,
France, Germany, Great Britain, Italy,
USA, ….
GRANTS
RFBR
DFG
CNRS
INTAS
IN2P3
Helmholtz Assosiation
UNESCO
Dynasty
FP6-NEST NANOCASE
PROGRAMMES:
Heisenberg-Landau
Votruba-Blokhincev
Bogoliubov-Infeld
Teaching Activity
Courses of lectures in
“Dubna” University, Moscow Phys.Tech.Inst., UNC JINR
– 7 (every year)
Courses of lectures on International Schools
~ 15 (every year)
Presentation of Theses:
Doctor of Science – 5
PhD – 4
We supervise diploma theses of students and postgraduate
students
Proposal for the new theme
”Modern mathematical physics:
gravity, supersymmetry, integrability”
Period of execution 2009–2013
Direction:
Theoretical Physics
Leaders:
Sorin A.S., Isaev A.P.
Scientific leader: Filippov A.T.
The superstring theory is generally accepted as the unique
candidate for the unified theory of all fundamental interactions,
including the quantum gravity. This theory as well as the
calculations beyond the perturbation theory in QFT are the key
subjects of modern mathematical physics. Development of the
methods appropriate for studying the whole complex of these
problems is in the focus of the proposal.
The main topics of the Theme include:
• study of superstring theory: different regimes, vacuums, classical and
quantum solutions;
• application of modern methods of mathematical physics to the
fundamental problems of theoretical physics: nonperturbative regime
of supersymmetric gauge theories, microscopic description of black
holes, cosmological models of early universe, investigation of
classical and quantum gravity;
• investigation of the new types of symmetries of physical models, such
as supersymmetries, quantum, nonlinear and infinite dimensional
symmetries.
The use of mathematical methods of the theory of
integrable systems, quantum groups, and noncommutative geometry is the decisive factor in
investigation of these problems.
Expected results
Construction and investigation of new supersymmetric models, unified theories
and models of fundamental interactions. Elaboration of new approaches to
investigation of nonperturbative regimes in quantum field theories, quantum
gravity and cosmology. Investigation of noncommutative gauge and
supersymmetric field theories on the base of the noncommutative geometry.
Development of mathematical methods for the theory of fundamental
interactions, in particular, the methods related to the integrable systems, theory
of symmetries, and noncommutative geometry. Application of these methods to
the construction and investigation of modern cosmological models.
The collaboration:
Australia, Armenia, Belgium, Bulgaria, Brazil, Great Britain, Hungary, Germany,
Greece, Georgia, India, Italy, Canada, Mexico, Poland, Russia, Rumania, USA,
Turkey, Ukraine, France, Czech Republic, Switzerland, Serbia, Croatia, Japan,
CERN, ICTP, SISSA.
Rector:
Leaders:
A.T. Filippov
A.S. Sorin, V.V. Voronov
DIAS-TH at JINR : Standing Activity



DIAS-TH is a substructure of BLTP supported by the JINR’s budget as one
of priority activities of the Institute.
DIAS-TH organizes and controls all educational programmes for young
scientists, graduates, and students.
DIAS-TH programme includes both the standing activity through the year
and the standard short schools (about 4 - 5 in a year).
The main goals of DIAS-TH:








training courses for young scientists, graduates and undergraduates
from the JINR MS and other countries
looking for and supporting gifted young theorists in the JINR Member States
creating databases of students and young researchers;
organization of schools of different level in Dubna
coordination with similar schools in the JINR MS, Germany, and other cntrs.
support of the JINR and CERN experimental programmes by organizing
lecture courses and lectures with a special emphasis on the LHC program
coordination with the schools and workshops supported by CERN, UNESCO,
ICTP, and other organizations
publication and distribution of lectures and discussions in different forms,
in particular, with the use of modern electronic means, etc.
Supported by
Supporting
up to 2005
In 2008, we have received the grant in the framework of
the UNESCO International Basic Science Programme
In 2004-2008, the following activities
in the framework of DIAS-TH were:
 Winter School on Theoretical Physics (2004--2008);
 International Student School on Selected Topics in Nuclear Theory (2004);
 Advanced Summer School on Modern Mathematical Physics (2004--2008);
 Research Workshop "Nucleation Theory and Applications" (2004--2008);
 School on Modern Cosmology and Astrophysics (2004);
 School on Heavy Quark Physics (2005, 2008);
 International School on Nuclear Theory and Astrophysical Applications (2005, 2007);
 School and Workshop on Calculations for Modern and Future Colliders (2006);
 School on Few-Body Problems in Physics (2006);
 School on Dense Matter in Heavy Ion Collisions and Astrophysics (2006, 2008)
Other activities:
 Lecture courses and review lectures on new trends in modern physics
were given for students and post-graduates.
 Computer processing of video records of lectures was carried out.
 A new lecture hall for DIAS-TH was opened.
 Web-site of DIAS-TH was opened and supported
http://theor.jinr.ru/~diastp/diasth
Prominent scientists
from JINR, Russia,
Ukraine,
Czechia,
and Germany were
invited as lecturers.
60 students and postgraduates from JINR,
Belarus,
Germany,
Kazakhstan, Poland,
Russia,
Romania,
Slovakia,
Ukraine,
and Czechia took part
in the School.
The School was attended by last-year
students of universities, post-graduate
students, and young scientists: 64
participants from Russia, Belorus,
Belgium,
Bolgaria,
Venezuela,
Germany, Spain, Poland, Ukraine, and
Chechia.
Lectures were given by the leading
scientists actively working on modern
problems
of
theoretical
and
mathematical physics: I. Buchbinder,
L. Cardoso, A. Filippov, E. Ivanov,
V. Rubakov, A. Starobinsky,
M. Vasiliev.
13
cycles
of
lectures
supplemented with seminars.
were
The program of three schools and research
workshop covered such fields of theoretical
physics as particle astrophysics, gravity and
cosmology, sypersymmetry and string theory,
conformal field theory, structure of an atomic
nucleus, nuclear reaction theory, halo nuclei,
properties of neutron stars, nucleosynthesis in
stars, properties of nuclear matter, critical
phenomena and nucleation theory.
The leading scientists from Canada, China,
Finland, Germany, Romania, Russia, Spain
and JINR gave more than 40 lecture courses
for about 170 PhD students and young
scientists from Armenia, Belarus,
China,Croatia, Czechia, Germany, Italy,
Japan, Poland, Russia,Turkey, Ukraine,
Uzbekistan, and JINR University Centre.
Activities were supported by the Helmholtz
Foundation, Russian Foundation for Basic
Research, Dinastiya Foundation and JINR.
2008 DIAS-TH Activity
The first school in this year:
Physics at the LHC, new
ideas and perspectives.
Special additional lectures
on modern technics,
accelerators, CERN
experimental facilities etc.
70 participants from Russia
and the JINR MS.
Two weeks of introductory
lectures and review talks
on new trends in modern
physics
You are welcome to the School!
Thank you
for attention!