We study the effective actions of various brane configurations in Matrix theory. Starting from the 0+1 dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories o

1Introduction

Matrixtheory[1]purportstobeacomplete,non-perturbativeformulationofMtheory.SinceagreatdealisknownaboutthephysicsofMtheoryinvariouscornersofmodulispace,muche orthasrecentlybeendirectedtowardsverifyingthatsuchphysicscanberecoveredfromMatrixtheory.InthispaperwewillbeprimarilyinterestedinstudyingthedescriptionofD-branesthatemergeswhenMatrixtheoryiscompacti edonacircle,yieldingthetypeIIAtheory.SomesalientfeaturesofD-branesinIIAtheorywhichonewouldliketoobtainfromMatrixtheoryincludethefollowing:thereexistDp-branesforp=0,2,4,6,8;thelowenergydynamicsofkparallelDp-branesisdescribedbyasupersymmetricp+1dimensionalU(k)gaugetheory;the(notnecessarilylowenergy)dynamicsofasingleD-braneisdescribedbyaBorn-Infeldtypeaction.Inaddition,oneknowsthesupergravity eldsproducedbyD-branesandsoalsothecorrespondingsmallanglescatteringamplitudesofseveralsuchobjects.

Banks,Seiberg,andShenker[2],andS.-J.Rey[3],tooksome rststepstowardsderivingthee ectiveactionsofD-branesfromMatrixtheory.Theyidenti edmatrixas-signmentscorrespondingtoD-branesbyidentifyingtheappropriatecentralchargesinthe11dimensionallightconegaugesupersymmetryalgebra.Thenbyanalyzingthe uctua-tionsaroundsuchbackgroundsandreplacinglargeNcommutatorsbyPoissonbrackets,theywereabletorecoverthegeneralstructureoftheknowne ectiveactionstoquadraticorderin elds.Here,ourgoalissimilar,butwewishtogobeyondquadraticorderandtokeepcarefultrackofnumericalfactors.Todososuccessfully,wefounditnecessarytoreplacematrixcommutatorsnotbyPoissonbracketsbutratherbythecommutatorsofcovariantderivatives,muchasonedoeswhenconsideringtoroidalcompacti cation.Bysodoing,weareabletoobtaingaugeinvariantactionswhichpreciselyreproducethe uctuationsoftheBorn-Infeldactioninthepresenceofalargebackgroundmagnetic eld.TherehavebeenanumberofstudiescomparingD-branescatteringamplitudesob-tainedfromMatrixtheoryandfromsupergravity.OntheMatrixtheoryside,theproce-

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