conformal field theory

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1、SergeiV.JCetovInstitutftiri%eor~ix&ePbysikUniversitiizHannoverGermanybWorldScientificbSingaporelNewJersey*LondonlHongKong._CPrefaceTheaimofphysicsasascienceistodescribethemostfundamentallawsofNature.Beingthemostfundamental,thephysicallawsaresimultaneouslythes

2、implestones.Tobesimpledoesnotmeanhowevertobetrivial.Thesimplicityoffundamentalphysicsexhibitsitselfinfundamentalsymmetryprinciples.Itisthereforefundamentalphysicalsymmetryprinciplesthatweshouldbelookingfor,anditismainlyatheoreticalproblem.Itisveryofteninphysi

3、csthatunderlyingsymmetriesarehiddenbythecomplexityofactualphysicalphenomena,anditistheobjectiveoftheoreticalphysicstouncoverthem.Takinghighenergyphysicsasanexample,thetheoreticalbasisforourcurrentunder-standingofpropertiesanddynamicsofelementaryparticlesispro

4、videdbyquantumfield*theory(QFT).AgeneralQFThoweverseemstobetoogeneralforthesepurposes.ItisthegaugeQFTsthatareapparentlydistinguishedindescribingfundamentalphysicalinteractionsofNature.ComparedtoageneralQFT,quantumgaugetheoriesaremuchmorerestrictiveandpossessa

5、dditionalsymmetries.Thewell-knownachievementsofgaugetheoriesinhighenergyphysicsduringlastdecadesperfectlyillustratethepowerofsymmetryprinciplesinphysics.Thehigheranenergyscale,themoresymmetricbecomeinteractionsamongelementaryparticles.Thisisaclearsignofsome(n

6、ormallybroken)symmetrywhichshouldbeformallyrestoredatinfiniteenergiesorvanishingmasses.Anotherrelevantexampleisprovidedbythetheoryofcriticalphenomena.Itisawell-knownfactthatquitedifferentphysicalsystemsattheircriticalityexhibituniver-salbehaviour.Thisalsoindi

7、catesapresenceofsomeunderlyingfundamentalsymmetry.Itistheconformalsymmetrythatisresponsibleinbothcases.Oneimportantpointshouldhoweverbeemphasized.Benefitsofhavingconformalsymmetryusuallycometrueintvodimensions,wherethissymmetrybecomesinfinite-dimensional.Anin

8、finitenumberofconservationlawsisresponsibleforanintegrabilityoftwo-dimensionalphysicalsystemspossessingconformalinvariance.Itisthetwo-dimensionalconformalfieldtheory(CFT)thatisactuallyadd