THEME01-3-1073-2009/2013

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01-3-1073-2009/2013

Priority:

Status:

In-progress

Modern Mathematical Physics: Gravity, Supersymmetry, Integrability

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

Participating Countries, Institutes and International organizations:
Australia, Austria, Armenia, Belarus, Belgium, Bulgaria, Brazil, Canada, CERN, China, Czech Republic, France, Germany, Greece, Hungary, ICTP, India, Italy, Japan, Mexico, Norway, Poland, Romania, Russia, Serbia, Turkey, Ukraine, United Kingdom, USA.

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 2010:

Construction of new superfield extensions of the integrable multiparticle Calogero models with N 4 supersymmetry within the approach based on gauging isometries of some free superfield Wess-Zumino models.

Development of a new off-shell N=3, d=3 harmonic superspace description of the combined N=6 Chern-Simons systems related to multiple M2 branes.
Investigation of new integrable spin chain models invariant under the action of orthogonal and symplectic quantum groups using the representation theory of Birman-Murakami-Wenzl algebras.

Futher development of the technique of generating series for Bethe vectors within the framework of the universal nested Bethe ansatz for quantum integrable models with linear symmetries. Calculation ofexplicit expressions for the norms of Bethe vectors.

Proof of Auroux conjecture related to Homological Mirror Symmetry for Fano varieties.
Construction and investigation of exact solutions in the dilaton gravity and search for the solution in supergravity corresponding to the integrable cosmological billiard.

Investigation of quantum effects generated by nontrivial geometry and topology of the space-time in the string theory and in the theory of multi-Universe.

Rigorous formulation of the spectral problem in quantum field theory on manifolds with nontrivial internal geometry and nontrivial geometry of boundaries by making use of the scattering formalism.

List of Activities
	Activity or Experiment	Leader
	Laboratory	Responsible person	Leading Researchers and number of participants
1.	Quantum groups and integrable systems	A.P. Isaev
	BLTP		R.M. Mir-Kasimov S.Z. Pakulyak G.S. Pogosyan P.N. Pyatov A.N. Sissakian N.A. Tyurin
2.	Supersymmetry	E.A. Ivanov
	BLTP		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
	BLTP		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
	LIT		I.L. Bogoliubsky A.M. Chervyakov E. Donets
	UC		S.Z. Pakuliak

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	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

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