Supersymmetry in Mathematics and Physics: UCLA Los Angeles, USA 2010

286 Pages·2011·1.44 MB·English

by  V. S. Varadarajan (auth.)

Lecture Notes in Mathematics 2027
Editors:
J.-M.Morel,Cachan
B.Teissier,Paris
Forfurthervolumes:
http://www.springer.com/series/304
•
Sergio Ferrara Rita Fioresi V.S. Varadarajan
(cid:2) (cid:2)
Editors
Supersymmetry
in Mathematics and Physics
UCLA Los Angeles, USA 2010
123
Editors
SergioFerrara RitaFioresi
CERN UniversityofBologna
De´pt.Physique DepartmentofMathematics
Div.The´orie PiazzaPortaSanDonato5
1211Gene`ve 40126Bologna
Switzerland Italy
[email protected] fi[email protected]
V.S.Varadarajan
UCLA
DepartmentofMathematics
520PortolaPlaza
LosAngeles,CA90095-1555
USA
[email protected]
ISBN978-3-642-21743-2 e-ISBN978-3-642-21744-9
DOI10.1007/978-3-642-21744-9
SpringerHeidelbergDordrechtLondonNewYork
LectureNotesinMathematicsISSNprintedition:0075-8434
ISSNelectronicedition:1617-9692
LibraryofCongressControlNumber:2011934804
MathematicsSubjectClassification(2010):81-XX;58A50;14A22;14M30;32C11
(cid:2)c Springer-VerlagBerlinHeidelberg2011
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Preface
Thearticlesinthiscollectionhavegrownoutofthetalksgivenata2-dayworkshop
on supersymmetryheld at UCLA in February 2010. The main theme of the Con-
ferencewas supersymmetryin mathematicsandphysics.Moreprecisely,the talks
attheconferencewerededicatedtosupersymmetryasaconnectingthemebetween
geometry,grouptheory,andfundamentalphysics.Inadditiontothespeakersthere
wereafewpostersdisplayedinapostersessionwhosecontentsarealsopresented
here.
Inanintroductiontothisvolumeabriefsurveyofsupersymmetryanditsmany
applications as developed in the articles of this volume is given. So we limit
ourselvestothankingthevariouspeopleandorganizationsthathavehelpedusand
madetheworkshopandthisvolumepossible.
First and foremost we thank the Department of Mathematics at UCLA for
providing all kinds of help and support, organizational, technical, and personal,
fortheconference.ToChairProfessorSorinPopaandChiefadministrativeperson
JudithLevin goesourgratitude.We wouldlike to thankBabette Daltonwho took
care of all the details of the conference; without her wholehearted cooperation
and tireless work the workshop could not have been arranged. We thank Jacquie
Bauwens for help during the 2 days of the workshop. We are also grateful to
the participants, whose lively interest and interactions with one another made the
workshop a great success. Last but not least, we thank profusely the people at
Springerwhowere mostforthcomingwith theiradvice,technicalandpersonal,as
wellastheircooperation,duringthepreparationofthisvolume.
Themainfinancialsupportcamefromananonymousdonorgrantwithmatching
fundsfromGoldman-Sachs,withnostringsattached.Weexpressourdeepgratitude
to them.Inadditionwe thankseveralinstitutionsandagenciesfortheirtraveland
othersupporttosomeoftheparticipants.
v
vi Preface
Finally, we thank the participants who providedus with the actual articles and
who responded to all our requests, large and small, with infinite patience and
courtesy.
SergioFerrara
RitaFioresi
V.S.Varadarajan
Contents
Introduction ...................................................................... 1
V.S.Varadarajan
BlackHolesandFirstOrderFlowsinSupergravity......................... 17
L.Andrianopoli,R.D’Auria,S.Ferrara,andM.Trigiante
RepresentationsofSuperLieGroups:SomeRemarks...................... 45
ClaudioCarmeliandGianniCassinelli
OnChiralQuantumSuperspaces.............................................. 69
D.Cervantes,R.Fioresi,andM.A.Lledo´
OntheConstructionofChevalleySupergroups.............................. 101
R.FioresiandF.Gavarini
IndecomposableFinite-DimensionalRepresentations
ofaClassofLieAlgebrasandLieSuperalgebras............................ 125
HansPlesnerJakobsen
OntheGeometryofSuperRiemannSurfaces................................ 139
StephenKwok
ChargeOrbitsandModuliSpacesofBlackHole
Attractors......................................................................... 155
AlessioMarrani
MaximalSupersymmetry ....................................................... 175
M.V.MovshevandA.Schwarz
LieSupergroups,UnitaryRepresentations,
andInvariantCones ............................................................. 195
Karl-HermannNeebandHadiSalmasian
vii
viii Contents
GeometryofDualPairsofComplex
Supercurves....................................................................... 241
JeffreyM.Rabin
OntheSuperdimensionofanIrreducibleRepresentation
ofaBasicClassicalLieSuperalgebra.......................................... 253
VeraSerganova
Contributors
L.Andrianopoli DipartimentodiFisica,PolitecnicodiTorino,CorsoDucadegli
Abruzzi24,10129Turin,Italy
and
INFN,SezionediTorino,Turin,Italy,[email protected]
Claudio Carmeli Universita` di Genova (Dipartimento di Fisica) and INFN
(sezione di Genova), Via Dodecaneso 33, 16146 Genova, Italy, claudio.
[email protected]
Gianni Cassinelli Universita` di Genova (Dipartimento di Fisica) and INFN
(sezione di Genova), Via Dodecaneso 33, 16146 Genova, Italy, cassinelli@ge.
infn.it
D.Cervantes InstitutodeCienciasNucleares,UniversidadNacionalAuto´nomade
Me´xico,CircuitoExterior,Me´xico,DF04510,Me´xico,[email protected]
R. D’Auria Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli
Abruzzi24,10129Turin,Italy
and
INFN,SezionediTorino,Turin,Italy,[email protected]
S. Ferrara Department of Physics, Theory Unit, CERN, 1211, Geneva 23,
Switzerland
and
INFN – Laboratori Nazionali di Frascati, 00044 Frascati, Rome, Italy, sergio.
[email protected]
R. Fioresi Dipartimento di Matematica, Universita` di Bologna, Piazza di Porta
SanDonato,5–40126Bologna,Italy,fi[email protected]
F. Gavarini Dipartimento di Matematica, Universita` di Roma “Tor Vergata,” via
dellaricercascientifica1–00133Rome,Italy,[email protected]
ix