THEME01-3-1047-2003/2007

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01-3-1047-2003/2007

Priority:

Status:

New

Modern Mathematical Physics

Leader:

A.T. Filippov
A.P. Isaev

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 2003:

Construction and investigation of the quantum three-dimensional integrable models: construction of the integral representations for dualized three-dimensional S-matrices; obtaining of the evolution operators and their spectra for the dualized three-dimensional integrable models.

Investigation of the ground state in the lattice GL_q(N) symmetric Perk-Schultz model for special value of the deformation parameter q ^N+1=1 and exploration of the behaviour of the corresponding stochastic lattice model in the stationary regime.

Investigation of the continuum limits of special matrix models (motivated by strings theories) and construction in these limits (non-Abelian) gauge field models.

Investigation and construction of the noncommutative gauge theories on the basis of the differential calculi on the quantum groups.
Constructing new, superbrane actions on the curved homogeneeous superbackgrounds, including the AdS one, studying of their relationships with superconformal field theories.

Working out convenient quantum methods in harmonic N=3 superspace, applying them to computing low-energy effective action of N=3 and N=4 gauge theories and checking the AdS/QFT correspondenece on this basis and establishing the relations with branes.

Investigation of integrable systems with N=2 and N=4 supersymmetries, and non-commutative deformations of the latter.
Application of the Liouville and Toda theory to constructing cosmological and black hole-like solutions of supergravity and to the algebraic understanding of compact and non compact supergravity gaugings.
Investigation of quantum cosmologies and black holes described by integrable 1+1 dimensional models.

Construction of open and periodic Toda lattice hierarchies with extended supersymmetries and investigation of their relevance to low-energy regimes of supersymmetric Yang Mills theories.

Development of the methods of spectral geometry and their applications to quantum gravity, field theory on background gravitational field, and to spectral problems with nonlinear dependence on the spectral parameter with applications to finite-temperature field theories in genearl stationary gravitational and gauge backgrounds.

Constructing of Hamiltonian for Lagrange systems with excplicit nonholonomic constrains and their quantization.

List of Activities
	Activity or project	Spokespersons	Principal researchers
1.	Quantum Groups and Integrable Systems	A.P. Isaev A.A. Vladimirov
			R.M. Mir-Kasimov S.Z. Pakulyak P.N. Pyatov S.M. Sergeev S.V. Shabanov C. Sochichiu V.P. Spiridonov N.A. Tyurin
2.	Supersymmetry	E.A. Ivanov
			S.O. Krivonos A.I. Pashnev A.O. Sutulin M.M. Tsulaia B.M. Zupnik
3.	Quantum Gravity, Cosmology and Strings	A.T. Filippov V.V. Nesterenko A.S. Sorin
			B.M. Barbashov V.B. Deryagin D.V. Fursaev T.A. Ivanova I.G. Pirozhenko A.D. Popov

Collaboration
Country or international organization	City	Institute or Laboratory
Armenia	Yerevan	YerPhI
		YSU
Australia	Adelaide	Univ.
Belgium	Leuven	K.U.Leuven
Brazil	San Paulo, SP	USP
Bulgaria	Sofia	INRNE BAS
		SU
Canada	Montreal	MGU
		UM
	Edmonton	UA
CERN
Czech Republic	Prague	CTU
		CU
		IP ASCR
	Rez	NPI ASCR
France	Annecy-le-Vieux	LAPP
	Dijon	UB
	Lyons	ENSLAPP
	Marseille	CPT
	Montpellier	Univ.
	Nantes	SUBATECH
	Orsay	LPTHE
	Paris	Univ. VI-VII
	Palaiseau	ETP
	Valenciennes	Univ.
Georgia	Tbilisi	RMI GAS
Germany	Berlin	FUB
		HUB
	Aachen	Univ.
	Bielefeld	Univ.
	Bonn	UniBonn
	Dortmund	UNIDO
	Erlangen	FAU
	Hannover	Univ.
	Jena	FSU
	Leipzig	Univ.
	Munich	MPI-P
	Potsdam	AEI
Greece	Athens	Univ.
Hungary	Budapest	KFKI RMKI
India	Calcutta	BI
ICTP
Italy	Bari	INFN
	Frascatti	INFN LNF
	Naples	INFN
	Padua	Univ.
	Pavia	INFN
	Pisa	INFN
	Salerno	Univ.
	Trieste	SISSA/ISAS
	Turin	INFN
Japan	Kyoto	KSU
		KU RIMS
		KU YITP
	Tsukuba	KEK
JINR	Dubna	LIT
Mexico	Leon	UG
Norway	Dragvoll	Univ.
Poland	Warsaw	CAC PAS
		WU
	Cracow	IP JU
		NINP
	Lodz	UL
	Wroclaw	UW
Romania	Bucharest	IFIN-HH
Russia	Moscow	MSU
		LPI RAS
		RRIMS
		SMI RAS
		SSC-ITEP
	Gatchina	PNPI RAS
	Petrozavodsk	PetrSU
	Protvino	SRC-IHEP
	St. Petersburg	POMI RAS
		PSU
	Tomsk	TSU
	Troitsk	INR RAS
Turkey	Istanbul	BU
United Kingdom	London	Imperial College
	Durham	Univ.
	Cambridge	Univ.
	Liverpool	Univ.
	Southampton	Univ.
	York	Univ.
Ukraine	Kiev	BITP NASU
	Dnepropetrovsk	DNU
	Kharkov	KFTI NASU
USA	New York, NY	RU
		CUNY
		SUNY
	Baltimore, MD	JHU
	Cincinnati, OH	UC
	Clemson, SC	CLEMSON
	Coral Gables, FL
	Minneapolis, MN	UofM
	Norman, OK	UO
	Philadelphia, PA	PENN
	Piscataway, NJ	RUTGERS
	Rochester, NY	UR
Yugoslavia	Belgrade	Univ.

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