THEME01-3-1047-2003/2007

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01-3-1047-2003/2007

Priority:

Status:

In-progress

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 2006:

Calculation of the universal weight functions for different series of simple Lie algebras and their application for the construction of the integral solutions for different versions of the difference Knizhnik-Zamolodchikov equations.

Construction of wave eigenfunctions in the generalized Ising model for the finite periodic chain.

Construction of dynamical models (like q-deformel Euler top) on the noncommutative spaces of the cotangent bundles over quantum groups. Calculation of the evolution operators for these models.

Finding explicit solutions of the reflection equations which describe spin models on the chains with nontrivial boundary conditions.
The geometric theory of supersymmetric higher spins in superspaces with tensorial coordinates will be developed including the approprite generalization of N=1 siupergravity in the Ogievetsky-Sokatchev approach.

New models of supersymmetric mechanics with global and local N=8 supersymmetry will be constructed, including their "fuzzy" versions, and their intrinsic relations with quantum Hall effect and higher-spin theory will be explored.

The quantum renormalization properties and geometric structure of supersymmetric theories with nonanticomutative deformations as well as their relationships with nontrivial bckgrounds in string theory will be explored in detail.
Investigation of the entanglement entropy in quantum critical phenomena and construction on this basis of the analogs of the models of quantum gravity.

Analysis of the integrable structure of the superstring field theory on the flat and maximally supersymmetric pp-wave background.

Analysis of the integrable structure of the superstring inspired supergravity cosmological models, and development of an algorithm of constructing their general solutions.

List of Activities
	Activity or Experiment	Leader	Principal researchers
1.	Quantum groups and integrable systems	A.A. Vladimirov A.P. Isaev
			R.M. Mir-Kasimov S.Z. Pakulyak G.S. Pogosyan P.N. Pyatov S.V. Shabanov A.N. Sissakian V.P. Spiridonov N.A. Tyurin
2.	Supersymmetry	E.A. Ivanov
			S.O. Krivonos 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
Australia	Adelaide	Univ.
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
Czech Republic	Prague	CTU
		CU
		IP ASCR
	Rez	NPI ASCR
France	Annecy-le-Vieux	LAPP
	Dijon	LPUB
	Lyons	ENS Lyon
	Marseille	CPT
	Montpellier	Univ.
	Nantes	SUBATECH
	Paris	LPTHE
		ENS
	Valenciennes	Univ.
Georgia	Tbilisi	RMI GAS
Germany	Berlin	FUB
		HUB
	Aachen	RWTH
	Bielefeld	Univ.
	Bonn	UniBonn
	Dortmund	Univ.
	Hannover	Univ.
	Jena	FSU
	Leipzig	Univ.
	Munich	MPI-P
	Potsdam	AEI
Greece	Athens	Univ.
Hong Kong	Hung Hom	PolyU
Hungary	Budapest	KFKI RMKI
India	Calcutta	BNC
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
		RIMS
		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
		VNIIMS
		SMI RAS
		SSC-ITEP
	Petrozavodsk	PetrSU
	Protvino	SRC-IHEP
	St. Petersburg	POMI
		SPbSU
	Tomsk	TPU
	Troitsk	INR RAS
Serbia and Montenegro	Belgrade	Univ.
Turkey	Istanbul	BU
	Izmir	IYTE
United Kingdom	London	Imperial College
	Durham	Univ.
	Cambridge	Univ.
	Liverpool	Univ.
	Southampton	Univ.
	York	Univ.
Ukraine	Kiev	BITP NASU
	Kharkov	KFTI NASU
USA	New York, NY	RU
		CUNY
		SUNY
	Baltimore, MD	JHU
	Cincinnati, OH	UC
	Clemson, SC	CLEMSON
	Caral Gables, FL	UM
	Minneapolis, MN	UofM
	Norman, OK	UO
	Philadelphia, PA	Penn
	Piscataway, NJ	Rutgers
	Rochester, NY	UR

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