THEME01-3-1073-2009/2013

Next theme	Prev. theme
to field of reseach	to contents

01-3-1073-2009/2013

Priority:

Status:

New

Modern Mathematical Physics: Gravity, Supersymmetry, Integrability

Leaders:	A.S. Sorin A.P. Isaev
Scientific leader:	A.T. Filippov

Scientific Programme:
Superstring Theory is the most serious and worldwide pursued candidate for a unified theory of all fundamental interactions including Quantum Gravity and thus it is the principal source of the problems which are the subject of modern mathematical physics. The development of the theory involves the study of its surprisingly wide spectrum of possible regimes, vacua and exact classical and quantum solutions. Furthermore, the theory has applications in many directions including the nonperturbative regime of supersymmetric gauge theories, the mechanics and thermodynamics of black holes and cosmological models of the universe expansion. These are unique laboratories to check general ideas from unified theories. In particular, in order to accommodate and develop the new ideas in these sectors inspired by String Theory, it is crucial to use the powerful mathematical methods provided by the theory of Integrable Systems, Quantum Groups and Non-Commutative Geometry. The goals of the present new theme precisely belong to the bridging between these fields and further development of suitable schemes to be applied in this context.

Expected main results in 2009:

Derivation of the formulas for the generating series of the norms for Bethe vectors by using the recently developed technique of generating series for Bethe vectors, in the framework of the universal nested Bethe ansatz for the quantum integrable models with gl_N symmetries.

Solution of the problem for projective plane by the hamiltonian methods in the framework of the problem of the Homological Mirror Symmetry for Fano varieties.

Investigation of the theory of representations of Birman-Murakami-Wenzl algebra. Construction and solution of the new integrable spin chain models with SO(N) and Sp(2N) symmetries on the basis of this represenatation theory.
Elaboration of a new off-shell N=3, d=3 harmonic superspace description of the combined N=6 Chern-Simons matter systems related to to multiple M2 branes. The superfield quantization in this superfield formulation and computation of quantum corrections to the original action.

Development of the most general "master" (or "root") superfield action of N=4 supersymmetric mechanics based on the most general nonlinear (4,4,0) multiplet, study of the associated target geometry. Derivation of the most general actions of the descendent multiplets with 4 physical fermions via the appropriate gaugings (abelian and/or nonabelian) of possible isometries of this action.

Construction of the new N=4 and N=8 supersymmetric superfield extensions of the integrable conformal Calogero model using the approach based on gauging isometries of some free superfield actions with Wess-Zumino terms.

Development of the new higher-spin particle models based on the Neveu-Schwarz formulation with additional bosonic tensor coordinates. Investigation of their relation to the previously known Green-Schwarz-type formulations.

Development of the bi-harmonic setting for the off-shell N=4 supersymetric mechanics and its application to the uniform description of the models involving both standard N=4, d=1 multiplets and their mirror counterparts.
Study of the black hole physics in the framework of one- and two-dimensional models of dilaton gravity. Investigation of the relationship between the static states, cosmological scenarios, and wave-like solutions.

Investigation of the microscopic origin of the Bekenstein-Howking entropy in the black hole physics.

Development of methods for calculation of the spectral zeta-functions and heat kernel.

List of Activities
	Activity or Experiment	Leader	Principal Researchers
1.	Quantum groups and integrable systems	A.P. Isaev
			R.M. Mir-Kasimov S.Z. Pakulyak G.S. Pogosyan P.N. Pyatov A.N. Sissakian N.A. Tyurin
2.	Supersymmetry	E.A. Ivanov
			S.A. Fedoruk S.O. Krivonos A.V. Shcherbakov A.O. Sutulin B.M. Zupnik
3.	Quantum gravity, cosmology and strings	A.T. Filippov V.V. Nesterenko A.S. Sorin
			B.M. Barbashov B. Dimitrov D.V. Fursaev V.V. Gribanov T.A. Ivanova A.B. Pestov I.G. Pirozhenko A.D. Popov E.A. Tagirov

Collaboration
Country or International Organization	City	Institute or Laboratory
Armenia	Yerevan	YSU
Austria	Vienna	TU Vienna
Australia	Adelaide	Univ.
Belarus	Minsk	IP NASB
Belgium	Leuven	K.U.Leuven
Brazil	San Paulo, SP	USP
Bulgaria	Sofia	INRNE BAS
		SU
Canada	Montreal	McGill
		UdeM
	Edmonton	U of A
CERN	Geneva
China	Hong Kong	PolyU
Czech Republic	Prague	CTU
		CU
		IP ASCR
	Rez	NPI ASCR
France	Annecy-le-Vieux	LAPP
	Dijon	LPUB
	Lyon	ENS Lyon
	Marseille	CPT
	Nantes	SUBATECH
	Paris	ENS
		LPTHE
	Palaiseau	Polytech
	Valenciennes	Univ.
Germany	Berlin	FU Berlin
		HUB
	Bielefeld	Univ.
	Bonn	UniBonn
	Dortmund	TU Dortmund
	Hannover	Univ.
	Jena	Univ.
	Leipzig	Univ.
	Munich	MPI-P
	Potsdam	AEI
Greece	Athens	Univ.
Hungary	Budapest	KFKI RMKI
India	Calcutta	BNC
ICTP
Italy	Bari	INFN
	Frascati	INFN LNF
	Naples	INFN
	Padua	Univ.
	Pavia	INFN
	Pisa	INFN
	Salerno	UniSa
	Trieste	SISSA/ISAS
	Turin	INFN
Japan	Fukuoka	Kyushu Univ.
	Kyoto	KSU
		RIMS
		YITP
	Tsukuba	KEK
Mexico	Leon	UG
Norway	Trondheim	NTNU
Poland	Warsaw	CAC PAS
		UW
	Cracow	IP JU
		NINP PAS
	Lodz	UL
	Wroclaw	UW
Romania	Bucharest	IFIN-HH
Russia	Moscow	ITEP
		LPI RAS
		MSU
		MI RAS
		VNIIMS
	Chernogolovka	LITP RAS
	Petrozavodsk	PetrSU
	Protvino	IHEP
	St. Petersburg	PDMI RAS
		SPbSU
	Tomsk	TPU
	Troitsk	INR RAS
Serbia	Belgrade	IP
		Univ.
Turkey	Istanbul	BU
	Izmir	IYTE
United Kingdom	London	Imperial College
	Cambridge	Univ.
	Durham	Univ.
	Liverpool	Univ.
	Southampton	Univ.
	York	Univ.
Ukraine	Kiev	BITP NASU
	Kharkov	KFTI NASU
USA	New York, NY	CUNY
		RU
		SUNY
	Baltimore, MD	JHU
	Cincinnati, OH	UC
	Clemson, SC	CLEMSON
	College Park, MD	UM
	Coral Gables, FL	UM
	Minneapolis, MN	UofM
	Philadelphia, PA	Penn
	Piscataway, NJ	Rutgers
	Rochester, NY	UR

Next theme	Prev. theme
to field of reseach	to contents