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M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect

A small number of M-theory branes as giant gravitons in the M-theory sector of LLM geometry is studied as a probe. The abelian way shows that the low energy effective action for M-theory brane is exactly the 2d electron subject to a vertical magnetic field

PreprinttypesetinJHEPstyle-HYPERVERSION

arXiv:hep-th/0607242v1 30 Jul 2006RanHuoShanghaiInstituteforAdvancedStudies,USTC99XiupuRoad,Nanhui,Shanghai,201315,P.R.ChinaandDepartmentofModernPhysics,USTCHefei,Anhui,230026,P.R.ChinaE-mail:huor@ustc.eduAbstract:AsmallnumberofM-theorybranesasgiantgravitonsintheM-theorysectorofLLMgeometryisstudiedasaprobe.Theabelianwayshowsthatthelowenergye ectiveactionforM-theorybraneisexactlythe2delectronsubjecttoaverticalmagnetic eld.Wealsobrie ydiscussthemicroscopicdescriptionofM2-branegiantgravitoninthisgeometry,inthelanguageofacombinationofD0-branesasfuzzy2-spheres.Thenwegotothewell-establishedNoncommutativeChern-Simonstheorydescription.Afterquantization,wellbehavedFractionalQuantumHallE ectisdemonstrated.ThisgoesbeyondtheoriginalLLMdescriptionandshouldbesomeindicationofnovelgeometry.

Keywords:Theories.

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