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INTEGRABILITY:FROMSTATISTICALSYSTEMSTOGAUGETHEORY
Integrability:FromStatisticalSystemsto GaugeTheory
Editedby
PatrickDorey,GregoryKorchemsky,NikitaNekrasov, VolkerSchomerus,DidinaSerban,LeticiaCugliandolo
GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom
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©OxfordUniversityPress2019
Themoralrightsoftheauthorshavebeenasserted
FirstEditionpublishedin2019
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LibraryofCongressControlNumber:2018967557
ISBN978–0–19–882815–0
DOI:10.1093/oso/9780198828150.001.0001
Printedandboundby CPIGroup(UK)Ltd,Croydon,CR04YY
LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork.
Previoussessions
I1951Quantummechanics.Quantumfieldtheory
II1952Quantummechanics.Statisticalmechanics.Nuclearphysics
III1953Quantummechanics.Solidstatephysics.Statisticalmechanics. Elementaryparticlephysics
IV1954Quantummechanics.Collisiontheory.Nucleon-nucleoninteraction. Quantumelectrodynamics
V1955Quantummechanics.Nonequilibriumphenomena.Nuclearreactions. Interactionofanucleuswithatomicandmolecularfields
VI1956Quantumperturbationtheory.Lowtemperaturephysics.Quantum theoryofsolids.Ferromagnetism
VII1957Scatteringtheory.Recentdevelopmentsinfieldtheory.Nuclearand stronginteractions.Experimentsinhighenergyphysics
VIII1958Themanybodyproblem
IX1959Thetheoryofneutralandionizedgases
X1960Elementaryparticlesanddispersionrelations
XI1961Lowtemperaturephysics
XII1962Geophysics;theearthsenvironment
XIII1963Relativitygroupsandtopology
XIV1964Quantumopticsandelectronics
XV1965Highenergyphysics
XVI1966Highenergyastrophysics
XVII1967Manybodyphysics
XVIII1968Nuclearphysics
XIX1969Physicalproblemsinbiologicalsystems
XX1970Statisticalmechanicsandquantumfieldtheory
XXI1971Particlephysics
XXII1972Plasmaphysics
XXIII1972Blackholes
XXIV1973Fluidsdynamics
XXV1973Molecularfluids
XXVI1974Atomicandmolecularphysicsandtheinterstellarmatter
XXVII1975Frontiersinlaserspectroscopy
XXVIII1975Methodsinfieldtheory
XXIX1976Weakandelectromagneticinteractionsathighenergy
vi Previoussessions
XXX1977Nuclearphysicswithheavyionsandmesons
XXXI1978Illcondensedmatter
XXXII1979Membranesandintercellularcommunication
XXXIII1979Physicalcosmology
XXXIV1980Laserplasmainteraction
XXXV1980Physicsofdefects
XXXVI1981Chaoticbehaviorofdeterministicsystems
XXXVII1981Gaugetheoriesinhighenergyphysics
XXXVIII1982Newtrendsinatomicphysics
XXXIX1982Recentadvancesinfieldtheoryandstatisticalmechanics
XL1983Relativity,groupsandtopology
XLI1983Birthandinfancyofstars
XLII1984Cellularandmolecularaspectsofdevelopmentalbiology
XLIII1984Criticalphenomena,randomsystems,gaugetheories
XLIV1985Architectureoffundamentalinteractionsatshortdistances
XLV1985Signalprocessing
XLVI1986Chanceandmatter
XLVII1986Astrophysicalfluiddynamics
XLVIII1988Liquidsatinterfaces
XLIX1988Fields,stringsandcriticalphenomena
L1988Oceanographicandgeophysicaltomography
LI1989Liquids,freezingandglasstransition
LII1989Chaosandquantumphysics
LIII1990Fundamentalsystemsinquantumoptics
LIV1990Supernovae
LV1991Particlesinthenineties
LVI1991StronglyinteractingfermionsandhighTc superconductivity
LVII1992Gravitationandquantizations
LVIII1992Progressinpictureprocessing
LIX1993Computationalfluiddynamics
LX1993Cosmologyandlargescalestructure
LXI1994Mesoscopicquantumphysics
LXII1994Fluctuatinggeometriesinstatisticalmechanicsandquantumfield theory
LXIII1995Quantumfluctuations
LXIV1995Quantumsymmetries
LXV1996Fromcelltobrain
LXVI1996Trendsinnuclearphysics,100yearslater
LXVII1997Modelingtheearthsclimateanditsvariability
LXVIII1997ProbingtheStandardModelofparticleinteractions
LXIX1998Topologicalaspectsoflowdimensionalsystems
LXX1998Infraredspaceastronomy,todayandtomorrow
LXXI1999Theprimordialuniverse
LXXII1999Coherentatomicmatterwaves
LXXIII2000Atomicclustersandnanoparticles
LXXIV2000Newtrendsinturbulence
LXXV2001Physicsofbio-moleculesandcells
LXXVI2001Unityfromduality:Gravity,gaugetheoryandstrings
LXXVII2002Slowrelaxationsandnonequilibriumdynamicsincondensed matter
LXXVIII2002Accretiondiscs,jetsandhighenergyphenomenainastrophysics
LXXIX2003Quantumentanglementandinformationprocessing
LXXX2003Methodsandmodelsinneurophysics
LXXXI2004Nanophysics:Coherenceandtransport
LXXXII2004MultipleaspectsofDNAandRNA
LXXXIII2005Mathematicalstatisticalphysics
LXXXIV2005ParticlephysicsbeyondtheStandardModel
LXXXV2006Complexsystems
LXXXVI2006Particlephysicsandcosmology:thefabricofspacetime
LXXXVII2007Stringtheoryandtherealworld:fromparticlephysicsto astrophysics
LXXXVIII2007Dynamos
LXXXIX2008Exactmethodsinlow-dimensionalstatisticalphysicsand quantumcomputing
XC2008Long-rangeinteractingsystems
XCI2009Ultracoldgasesandquantuminformation
XCII2009Newtrendsinthephysicsandmechanicsofbiologicalsystems
XCIII2009ModernperspectivesinlatticeQCD:quantumfieldtheoryand highperformancecomputing
XCIV2010Many-bodyphysicswithultra-coldgases
XCV2010Quantumtheoryfromsmalltolargescales
XCVI2011Quantummachines:measurementcontrolofengineered quantumsystems
XCVII2011TheoreticalphysicstofacethechallengeofLHC
SpecialIssue2012Advanceddataassimilationforgeosciences
XCVIII2012Softinterfaces
XCIX2012Stronglyinteractingquantumsystemsoutofequilibrium
C2013Post-Planckcosmology
CI2013Quantumopticsandnanophotonics
SpecialIssue2013Statisticalphysics,optimization,inferenceandmessage-passing algorithms
CII2014Frommoleculestolivingorganisms:Aninterplaybetween biologyandphysics
CIII2014Topologicalaspectsofcondensedmatterphysics
CIV2015Stochasticprocessesandrandommatrices
CV2015Quantumoptomechanicsandnanomechanics
CVI2016Integrability:fromstatisticalsystemstogaugetheory
CVII2016Currenttrendsinatomicphysics
viii Previoussessions
Publishers
—SessionVIII:Dunod,Wiley,Methuen —SessionsIXandX:Herman,Wiley
—SessionXI:GordonandBreach,PressesUniversitaires —SessionsXII–XXV:GordonandBreach —SessionsXXVI–LXVIII:NorthHolland
—SessionLXIX–LXXVIII:EDPSciences,Springer —SessionLXXIX–LXXXVIII:Elsevier
—SessionLXXXIX–:OxfordUniversityPress
ListofParticipants xv
1Integrabilityinstatisticalphysicsandquantumspinchains 1 JesperLykkeJacobsen
2Aguidetotwo-dimensionalconformalfieldtheory 60 JörgTeschner
3Lecturesontheholographicdualityofgaugefieldsandstrings 121 GordonW.Semenoff
4Introductiontoscatteringamplitudes 183 DavidKosower
5Integrabilityinsigma-models 205 K.Zarembo
6Integrabilityin2Dfieldstheory/sigma-models 248 SergeiL.LukyanovandAlexanderB.Zamolodchikov
7Applicationsofintegrablemodelsincondensedmatter andcoldatomphysics 319 FabianH.L.Essler
8Introductiontointegrabilityandone-pointfunctionsin N = 4 supersymmetricYang–Millstheoryanditsdefectcousin 352 MariusdeLeeuw,AsgerC.Ipsen, CharlotteKristjansen,andMatthiasWilhelm
9Spectrumof N = 4 supersymmetricYang–Millstheoryandthe quantumspectralcurve 400 NikolayGromov
10Three-pointfunctionsin N = 4 supersymmetricYang–Millstheory 449 ShotaKomatsu
11Localizationand N = 2 supersymmetricfieldtheory 501 VasilyPestun
AppendixA:Lecturesgivenattheschoolbutnowrittencontribution 541 SlavaRychkov Conformalfieldtheoryinhigherdimensions
Contents
LeonardoRastelli
VladimirKazakov
ListofParticipants
Organizers
LeticiaCUGLIANDOLO
PatrickDOREY
DepartmentofMathematicalSciences,DurhamUniversity,LowerMountjoy,Stockton Road,DurhamDH13LE,UnitedKingdom
GregoryKORCHEMSKY
InstitutdePhysiqueThéorique,Saclay,UMR3681CNRS,bat774Saclay,F-91191 Gif-sur-Yvette,France
NikitaNEKRASOV
SimonsCenterforGeometryandPhysics,StonyBrookUniversity,StonyBrookNY 11794-3636USA
VolkerSCHOMERUS
DESYTheoryGroup,DESYHamburg,Notkestraße85,D-22607Hamburg,Germany
DidinaSERBAN
InstitutdePhysiqueThéorique,Saclay,UMR3681CNRS,bat774Saclay,F-91191 Gif-sur-Yvette,France
Lecturers
BenjaminBASSO
LaboratoiredePhysiqueThéorique,ÉcoleNormaleSupérieure,24RueLhomond, 75005Paris,France
VladimirBAZHANOV
DepartmentofTheoreticalPhysics,ResearchSchoolofPhysicsandEngineering, AustralianNationalUniversity,Canberra,ACT2601,Australia
MariusDELEEUW
NielsBohrInstitute,CopenhagenUniversityBlegdamsvej17,DK-2100Copenhagen
xvi ListofParticipants
FabianH.L.ESSLER
TheRudolfPeierlsCentreforTheoreticalPhysics,OxfordUniversity,Oxford,OX1 3NP,UnitedKingdom
PaulFENDLEY
TheRudolfPeierlsCentreforTheoreticalPhysics,OxfordUniversity,Oxford,OX1 3NP,UnitedKingdom
NikolayGROMOV
MathematicsDepartment,King’sCollegeLondon,TheStrand,LondonWC2R2LS, UnitedKingdom
AsgerC.IPSEN
NielsBohrInstitute,CopenhagenUniversityBlegdamsvej17,DK-2100Copenhagen
JesperLykkeJACOBSEN
LaboratoiredePhysiqueThéorique,ÉcoleNormaleSupérieure,24RueLhomond, 75005Paris,France
VladimirKAZAKOV
LaboratoiredePhysiqueThéorique,ÉcoleNormaleSupérieure,24RueLhomond, 75005Paris,France
ShotaKOMATSU
SchoolofNaturalSciences,InstituteforAdvancedStudy,Princeton,NewJerseyUSA
IvanKOSTOV
InstitutdePhysiqueThéorique,Saclay,UMR3681CNRS,bat774Saclay,F-91191 Gif-sur-Yvette,France
DavidKOSOWER
InstitutdePhysiqueThéorique,Saclay,UMR3681CNRS,bat774Saclay,F-91191 Gif-sur-Yvette,France
CharlotteKRISTJANSEN
NielsBohrInstitute,CopenhagenUniversity,Blegdamsvej17,2100Copenhagen, Denmark
SergeiL.LUKYANOV
NHETC,DepartmentofPhysicsandAstronomy,RutgersUniversity,Piscataway,NJ 08855-0849,USA
AndreiOKOUNKOV
ColumbiaUniversity,NewYork,USA
VasilyPESTUN
InstitutdesHautesÉtudesScientifiques,Bures-sur-Yvette,France
ListofParticipants
LeonardoRASTELLI
C.N.YangInstituteforTheoreticalPhysics,StonyBrookUniversity,StonyBrook, 11794,NY,USA
SlavaRYCHKOV
LaboratoiredePhysiqueThéorique,ÉcoleNormaleSupérieure,24RueLhomond, 75005Paris,France
GordonW.SEMENOFF
DepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,Vancouver,BC V6T1Z1Canada
JörgTESCHNER
DepartmentofMathematics,UniversityofHamburg,Bundesstrasse55,20146Hamburg,Germany
PedroVIEIRA
PerimeterInstituteforTheoreticalPhysics,Waterloo,OntarioN2L2Y5,Canada
MatthiasWILHELM
NielsBohrInstitute,CopenhagenUniversityBlegdamsvej17,DK-2100Copenhagen
AlexanderB.ZAMOLODCHIKOV
NHETC,DepartmentofPhysicsandAstronomy,RutgersUniversity,Piscataway,NJ 08855-0849,USA
KonstantinZAREMBO
Nordita,KTHRoyalInstituteofTechnologyandStockholmUniversity,Roslagstullsbacken23,SE-10691Stockholm,Sweden
PaulZINN-JUSTIN
SchoolofMathematicsandStatistics,TheUniversityofMelbourne,Parkville,Victoria 3010,Australia
StudentsandAuditors
JeremiasAGUILERADAMIA
InstitutodeF ´ sicadeLaPlata(IFLP),CONICET,UniversidadNacionaldeLaPlata, Argentina
MikhailALFIMOV
ÉcoleNormaleSupérieure,LaboratoiredePhysiqueThéorique,24rueLhomond, 75231Paris,FranceandInstitutdePhysiqueThéoriqueCEASaclay,Ormedes Merisiersbâtiment774,Pointcourrier136,F-91191Gif-sur-YvetteCedex,France
RodrigoALVESPIMENTA
CentrodeCiênciasExtasedeTecnologia-UniversidadeFederaldeSãoCarlosRodovia WashingtonLuis,km235,SaoCarlos-SP-Brasil
xviii ListofParticipants
RaphaëlBELLIARD
CEASaclay,InstitutdePhysiqueThéorique,OrmedesMerisiersbâtiment774,Point courrier136,F-91191Gif-sur-YvetteCedex,France
LorenzoBIANCHI
II.InstitutfürTheoretischePhysik,UniversitätHamburg,LuruperChaussee149,22761 Hamburg,Germany
IsakBUHL-MORTENSEN
TheNielsBohrInstitute,Blegdamsvej17,2100København,Denmark
DmitryBYKOV
Max-Plank-InstitutfuerGravitationsphysik,AmMuehlenberg1,D-1476,PostdamGolm,Germany
AlessandraCAGNAZZO
NORDITA,Roslagstullsbacken23,10691Stockholm,SwedenandDESY,Theory GroupNotkestrasse8,Bldg.2aD-22607Hamburg,Germany
RobertCARCASSEÉSQUEVEDO
UniversidadedoPorto,FaculdadedeCiências,RuadoCampoAlegre1021/1055,4169007Porto,Portugal
AndreaCAVAGLIA
PhysicsDepartment,UniversityofTorino,DipartimentodiFisica,viaPietroGiuria1, 10125,Torino,Italy
VsevolodCHESTNOV
DESY,Notkestraße85,D-22607Hamburg,Germany
MartinaCORNAGLIOTTO
DESYNotkestraße8522607Hamburg,bad.2Aroom306,Germany
FrankCORONADO
PerimeterInstituteforTheoreticalPhysics,31CarolineStreetNorth,Waterloo,ONN2L 2Y5,Canada
AlejandroDELAROSAGOMEZ
UniversityofYork,Heslington,YorkYO105DD,UnitedKingdom
AlejandroDELAROSAGOMEZ
UniversityofYork,Heslington,YorkYO105DD,UnitedKingdom
OlgaDIMITROVA
LandauInstituteforTheoreticalPhysics,KosyginaStreet2,119334Moscow,Russia
StefanDRUC
UniversityofSouthampton,SchoolofPhysicsandAstronomy,46/4119UniversityRd, SouthamptonSO171BJ,UnitedKingdom
ListofParticipants xix
GyorgyFEHER
LPTHE-CNRS-UPMC,Boîte126,T13-144èmeétage,4placeJussieu75252Paris CEDEX05,France
RouvenFRASSEK
DepartmentofMathematicalSciences,DurhamUniversity,LowerMountjoy,Stockton Road,DurhamDH13LE,UnitedKingdom
OleksandrGAMAYUN
NielsBohrweg2,Leiden,NL-2333CA,TheNetherlands
AlexandrGARBALI
ACEMS,SchoolofMathematicsandStatistics,TheUniversityofMelbourne,Victoria 3010,Australia
PavloGAVRYLENKO
7,Vavilovastr.,Moscow,Russia,117312
VictorGIRALDORIVERA
ICTPStradaCostiera11,34151,Trieste,Italy
TamásGOMBOR
WignerResearchCentreforPhysicsofH.A.S,29-33KonkolyThegeMiklósút, Budapest,XII.,H-1121andInstituteofTheoreticalPhysics,EötvösLorándUniversity, 1518Budapest,Pf.32.Hungary
LuciaGOMEZCORDOVA
PerimeterInstituteforTheoreticalPhysics,31CarolineStreetNorth,Waterloo,ONN2L 2Y5,Canada
GuzmanHERNANDEZ
CenterforCosmologyandParticlePhysics,PhysicsDepartment,NewYorkUniversity, 4WashingtonPlace,Room424,NewYork,NY10003,USA
LorenzHILFIKER
UniversitätHamburg,DepartmentofMathematics,Bundesstrasse55,20146Hamburg, Germany
AsgerIPSEN
TheNielsBohrInstitute,UniversityofCopenhagen,Blegdamsvej17,2100Copenhagen, Denmark
MikhailISACHENKOV
DepartmentofParticlePhysicsandAstrophysics,WeizmannInstituteofScience, Rehovot7610001,Israel
SaebyeokJEONG
DepartmentofPhysicsandAstronomy,StonyBrookUniversity,StonyBrook,NY 11790,USA
YunfengJIANG
InstituteforTheoreticalPhysics,ETHZurich,Wolfgang-PauliStrasse27,8093Zurich, Switzerland
RobKLABBERS
II.InstituteforTheoreticalPhysics,HamburgUniversity,Germany
GlebKOTOUSOV
RutgersUniversity,NHETC,Rutgers,TheStateUniversityofNewJersey,126FrelinghuysenRd,Piscataway,NJ08854-8019,USA
SylvainLACROIX
LaboratoiredePhysique(UMRCNRS5672),ÉcoleNormaleSupérieuredeLyon,46, alléed’Italie,F-69364F-69364Lyon,France
JulesLAMERS
InstituteforTheoreticalPhysics,UtrechtUniversity,Leuvenlaan4,3584CEUtrecht, TheNetherlands
FedorLEVKOVICH-MASLYUK
King’sCollegeLondon,MathematicsDepartment,TheStrand,WC2R2LSLondon, UnitedKingdom
AndriiLIASHYK
NationalResearchUniversityHigherSchoolofEconomics,FacultyofMathematics, MathematicalPhysicsDept.,7VavilovaStr.,Moscow,Russia
ChristianMARBOE
TrinityCollegeDublin,CollegeGreen2,Dublin2,Ireland
MarkoMEDENJAK
FacultyofMathematicsandPhysics,UniversityofLjubljana,Jadranska19,SI-1000 Ljubljana,Slovenia
DanielRicardoMEDINARINCON
Nordita-NordicInstituteforTheoreticalPhysics,Roslagstullsbacken23,10691Stockholm,Sweden
DavidMEIDINGER
InstitutfürMathematikundInstitutfürPhysik,Humboldt-UniversitätzuBerlin,IRIS Gebäude,ZumGroßenWindkanal6,12489Berlin,Germany
VladimirMITEV
InstitutfürPhysik,WATHEP,JohannesGutenbergUniversityMainz,Staudingerweg7, 55128Mainz,Germany
DennisMÜLLER
Humboldt-UniversitätzuBerlin,InstitutfürPhysik,AGQuantenfeld-undStringtheorie, ZumGroßenWindkanal6,D-12489Berlin,Germany
ListofParticipants
HagenMÜNKLER
Humboldt-UniversityBerlin,Germany
JuanMIGUELNIETOGARCÍA
InstitutdePhysiqueThéorique,OrmedesMerisiersbatiment774,Pointcourrier136, F-91191Gif-sur-YvetteCedex,France
BaptistePEZELIER
LaboratoiredePhysiquedel’ENSdeLyon,46alléed’Italie,F-69364Lyon,France
ElliPOMONI
DESY,TheoryGroup,Notkestrasse85,Bldg.2a,D-22607Hamburg,Germany
DariaRUDNEVA
MathDepartmentatHigherSchoolofEconomics,Vavilovastreet7,Moscow,Russia
NaveenSUBRAMANYAPRABHAKAR
C.N.YangInstituteforTheoreticalPhysics,DepartmentofPhysicsandAstronomy, StonyBrookUniversity,StonyBrook,NY11794-3800,USA
IstvánM.SZÉCSÉNYI
DepartmentofMathematicalSciences,DurhamUniversity,LowerMountjoy,Stockton Road,DurhamDH13LE,UnitedKingdom
Vuong-VietTRAN
DepartmentofMathematicalSciences,DurhamUniversity,LowerMountjoy,Stockton Road,DurhamDH13LE,UnitedKingdom
AdamVARGA
CityUniversityLondon,NorthamptonSquare,LondonEC1V0HB,UnitedKingdom
ErikWIDÉN
Nordita,Roslagstullsbacken23,10691Stockholm,Sweden
RuidongZHU
UniversityofTokyo,7-3-1Hongo,Bunkyo,Tokyo,Japan
LeonardZIPPELIUS
InstitutfürPhysik,HumboldtUniversitätzuBerlin,UnterdenLinden6,10099Berlin, Germany
