Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2013

554 Pages·2014·6.342 MB·English

by  Vladimir Dobrev (eds.)

Springer Proceedings in Mathematics & Statistics
Vladimir Dobrev E ditor
Lie Theory and
Its Applications
in Physics
Varna, Bulgaria, June 2013
Springer Proceedings in Mathematics & Statistics
Volume 111
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Vladimir Dobrev
Editor
Lie Theory and Its
Applications in Physics
Varna, Bulgaria, June 2013
123
Editor
VladimirDobrev
InstituteforNuclearResearch
andNuclearEnergy
BulgarianAcademyofSciences
72TsarigradskoChaussee
Sofia,Bulgaria
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-4-431-55284-0 ISBN978-4-431-55285-7(eBook)
DOI10.1007/978-4-431-55285-7
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Preface
The Workshop series ‘Lie Theory and Its Applications in Physics’ is designed
to serve the community of theoretical physicists, mathematical physicists and
mathematicians working on mathematical models for physical systems based on
geometricalmethodsandinthefieldofLietheory.
The series reflects the trend towards a geometrisation of the mathematical
description of physical systems and objects. A geometric approach to a system
yieldsingeneralsomenotionofsymmetrywhichisveryhelpfulinunderstanding
its structure. Geometrisation and symmetries are meant in their widest sense, i.e.,
representation theory, algebraic geometry, infinite-dimensional Lie algebras and
groups, superalgebras and supergroups, groups and quantum groups, noncom-
mutative geometry, symmetries of linear and nonlinear PDE, special functions.
Furthermore we include the necessary tools from functional analysis and number
theory.Thisisabiginterdisciplinaryandinterrelatedfield.
The first three workshops were organised in Clausthal (1995, 1997, 1999), the
4thwaspartofthe2ndSymposium‘QuantumTheoryandSymmetries’inCracow
(2001),the5th,7th,8thand9thwereorganisedinVarna(2003,2007,2009,2011),
the6thwaspartofthe4thSymposium‘QuantumTheoryandSymmetries’inVarna
(2005),buthasitsownvolumeofProceedings.
The 10th Workshop of the series (LT-10) was organized by the Institute of
NuclearResearchandNuclearEnergyoftheBulgarianAcademyofSciences(BAS)
inJune2013(17–23),attheGuestHouseofBASnearVarnaontheBulgarianBlack
SeaCoast.
Theoverallnumberofparticipantswas71andtheycamefrom21countries.
The scientific level was very high as can be judged by the speakers. The
plenary speakers were: Loriano Bonora (Trieste), Branko Dragovich (Belgrade),
Ludvig Faddeev (St. Petersburg), Malte Henkel (Nancy), Evgeny Ivanov (Dubna),
Toshiyuki Kobayashi (Tokyo), Ivan Kostov (Saclay), Karl-Hermann Neeb (Erlan-
gen), Eric Ragoucy (Annecy), Ivan Todorov (Sofia), Joris Van Der Jeugt (Ghent),
GeorgeZoupanos(Athens).
The topics covered the most modern trends in the field of the Workshop:
Symmetries in String Theories and Gravity Theories, Conformal Field Theory,
v
vi Preface
Integrable Systems, Representation Theory, Supersymmetry, Quantum Groups,
VertexAlgebrasandSuperalgebras,QuantumComputing.
There is some similarity with the topics of preceding workshops, however, the
comparison shows how certain topics evolve and that new structures were found
andused.Forthepresentworkshopwementionmoreemphasison:representation
theory, quantum groups, integrable systems, vertex algebras and superalgebras,
on conformal field theories, applications to the minimal supersymmetric standard
model.
The International Organizing Committee was: V.K. Dobrev (Sofia) and H.-D.
Doebner(Clausthal)incollaborationwithG.Rudolph(Leipzig).
The Local Organizing Committee was: V.K. Dobrev (Chairman), V.I. Doseva,
A.Ch. Ganchev, S.G. Mihov, D.T. Nedanovski, T.V. Popov, T.P. Stefanova, M.N.
Stoilov,N.I.Stoilova,S.T.Stoimenov.
Acknowledgments
Weexpressourgratitudetothe
– InstituteofNuclearResearchandNuclearEnergy
– AbdusSalamInternationalCentreforTheoreticalPhysics
for financial help. We thank the Bulgarian Academy of Sciences for providing its
Guest House which contributed very much to the stimulating and pleasant atmo-
sphere during the Workshop. We thank the Publisher, Springer Japan, represented
byMs.ChinoHasebe(ExecutiveEditorinMathematics,Statistics,Business,Eco-
nomics, Computer Science) and Mr. Masayuki Nakamura (Editorial Department),
forassistanceinthepublication.Last,butnotleast,IthankthemembersoftheLocal
OrganizingCommitteewho,throughtheirefforts,madetheworkshoprunsmoothly
andefficiently.
Sofia,Bulgaria VladimirDobrev
May2014
Contents
PartI PlenaryTalks
RevisitingTraceAnomaliesinChiralTheories............................... 3
LorianoBonora,StefanoGiaccari,andBrunoLimaDeSouza
CompleteT-DualizationofaStringinaWeaklyCurvedBackground..... 13
Lj.Davidovic´,B.Nikolic´,andB.Sazdovic´
ModularDoubleoftheQuantumGroupSL (2,R)........................... 21
q
L.D.Faddeev
Physical Ageing and New Representations of Some
LieAlgebrasofLocalScale-Invariance........................................ 33
MalteHenkelandStoimenStoimenov
NewTypeofN D4SupersymmetricMechanics ............................ 51
EvgenyIvanovandStepanSidorov
Vector-Valued Covariant Differential Operators
fortheMöbiusTransformation................................................. 67
ToshiyukiKobayashi,ToshihisaKubo,andMichaelPevzner
Semi-classicalScalarProductsintheGeneralisedSU(2)Model............ 87
IvanKostov
WeakPoissonStructuresonInfiniteDimensionalManifolds
andHamiltonianActions........................................................ 105
K.-H.Neeb,H.Sahlmann,andT.Thiemann
BetheVectorsofgl(3)-InvariantIntegrableModels,
TheirScalarProductsandFormFactors ..................................... 137
EricRagoucy
vii
viii Contents
PolylogarithmsandMultizetaValuesinMasslessFeynmanAmplitudes.. 155
IvanTodorov
Reduction of Couplings in Quantum Field Theories
withApplicationsinFiniteTheoriesandtheMSSM......................... 177
S.Heinemeyer,M.Mondragón,N.Tracas,andG.Zoupanos
PartII StringTheoriesandGravityTheories
ASUSYDouble-WellMatrixModelas2DTypeIIASuperstring.......... 199
FumihikoSugino
f.R/-Gravity:“EinsteinFrame”LagrangianFormulation,
Non-standardBlackHolesandQCD-LikeConfinement/Deconfinement.. 211
E.Guendelman,A.Kaganovich,E.Nissimov,andS.Pacheva
TheD-BraneChargesofC /Z ................................................. 223
3 2
ElaineBeltaos
OnRobertsonWalkerSolutionsinNoncommutativeGaugeGravity...... 231
SimonaBabeti
SomePower-LawCosmologicalSolutionsinNonlocal
ModifiedGravity................................................................. 241
Ivan Dimitrijevic, Branko Dragovich, Jelena Grujic,
andZoranRakic
OnNonlocalModifiedGravityandCosmology............................... 251
BrankoDragovich
PartIII IntegrableSystems
VertexOperatorApproachtoSemi-infiniteSpinChain:
RecentProgress .................................................................. 265
TakeoKojima
ThermopowerintheCoulombBlockadeRegimeforLaughlin
QuantumDots.................................................................... 279
LachezarS.Georgiev
OnaPairofDifferenceEquationsforthe F TypeOrthogonal
4 3
PolynomialsandRelatedExactly-SolvableQuantumSystems ............. 291
E.I.Jafarov,N.I.Stoilova,andJ.VanderJeugt
SpinChainModelsofFreeFermions.......................................... 301
Cˇ.Burdík,A.P.Isaev,S.O.Krivonos,andO.Navrátil
Group Analysis of Generalized Fifth-Order Korteweg–de
VriesEquationswithTime-DependentCoefficients.......................... 311
OksanaKuriksha,SeverinPošta,andOlenaVaneeva
Contents ix
A Construction of Generalized Lotka–Volterra Systems
Connectedwithsl (C) ........................................................... 323
n
S.A.Charalambides,P.A.Damianou,andC.A.Evripidou
Systems of First-Order Ordinary Differential Equations
InvariantwithRespecttoLinearRealizations
ofTwo-andThree-DimensionalLieAlgebras................................ 331
OksanaKuriksha
PartIV SupersymmetryandQuantumGroups
OnPrincipalFiniteW-AlgebrasforCertainOrthosymplectic
LieSuperalgebrasandF(4)..................................................... 343
ElenaPoletaeva
Super-deSitterandAlternativeSuper-PoincaréSymmetries............... 357
V.N.Tolstoy
Localizations of U (sl(2)) and U (osp(1j2)) Associated
q q
withEuclideanandSuperEuclideanAlgebras............................... 369
PatrickMoylan
Onthe2DZeroModes’AlgebraoftheSU(n)WZNWModel.............. 381
LudmilHadjiivanovandPaoloFurlan
PartV ConformalFieldTheories
Breakingso(4)SymmetryWithoutDegeneracyLift......................... 395
M.Kirchbach,A.PallaresRivera,andF.deJ.RosalesAldape
OntheRelationBetweenanN D1SupersymmetricLiouville
FieldTheoryandaPairofNon-SUSYLiouvilleFields...................... 405
LeszekHadaszandZbigniewJaskólski
Multi-Point Virtual Structure Constants and Mirror
ComputationofCP2-Model..................................................... 415
MasaoJinzenji
N-ConformalGalileanGroupasaMaximalSymmetryGroup
ofHigher-DerivativeFreeTheory.............................................. 425
KrzysztofAndrzejewskiandJoannaGonera
PartVI VertexAlgebrasandSuperalgebras
Virasoro Structures in the Twisted Vertex Algebra
oftheParticleCorrespondenceofTypeC..................................... 435
IanaI.Anguelova