M-theory on G_2 manifolds and the method of (p,q) brane webs

M-theory on G_2 manifolds and the method of (p,q) brane webs

GNPHE/03-04

hep-th/0303198

arXiv:hep-th/0303198v3 25 Mar 2004M-theoryonG2manifoldsandthemethodof(p,q)branewebsAdilBelhajNationalGroupingofHighEnergyPhysics,GNPHEandLab/UFRHighEnergyPhysics,DepartmentofPhysicsFacultyofSciences,Rabat,MoroccoDepartmentofMathematicsandStatistics,ConcordiaUniversityMontr´eal,Qu´ebec,CanadaH4B1R6February1,2008AbstractUsingareformulationofthemethodof(p,q)webs,westudythefour-dimensionalN=1quivertheoriesfromM-theoryonseven-dimensionalmanifoldswithG2holon-

omy.We rstconstructsuchmanifoldsasU(1)quotientsofeight-dimensionaltorichyper-K¨ahlermanifolds,usingN=4supersymmetricsigmamodels.Weshowthatthesegeometries,ingeneral,aregivenbyrealconesonS2bundlesovercomplextwo-dimensionaltoricvarieties,V2=Cr+2/C r.ThenwediscusstheconnectionbetweenthephysicscontentofM-theoryonsuchG2manifoldsandthemethodof(p,q)webs.Mo-tivatedbyaresultofAcharyaandWitten[hep-th/0109152],wereformulatethemethodof(p,q)websandreconsiderthederivationofthegaugetheoriesusingtoricgeometryMorivectorsofV2andbranechargeconstraints.ForWP2w1,w2,w3,we ndthatthe

gaugegroupisgivenbyG=U(w1n)×U(w2n)×U(w3n).Thisisrequiredbytheanomalycancellationcondition.

KEYWORDS:M-theory,G2manifolds,Toricgeometry.