M-theory on G_2 manifolds and the method of (p,q) brane webs(17)
发布时间：2021-06-11
M-theory on G_2 manifolds and the method of (p,q) brane webs
gaugesystems.Thelatterhavearemarkablefeaturewhichhasaniceinterpretationusingtherecentderivationoflocalmirrorsymmetryintwo-dimensional eldtheorywithN=2supersymmetry[39].Indeed,intheabovetwoexamples,ficanbewrittenasfollows
f1=w2w3d
f2=w1w3d
f3=w1w2d
wheredisthedegreeofthefollowinghomogeneousLGCalabi-Yausuperpotentials
y2+x4+z4+etxyz=0
y2+x3+z6+etxyz=0(5.6)(5.5)
mirrortotypeIIBN=2sigmamodelontheanti-canonicallinebundlesoverWP21,2,1andWP21,2,3respectively.
6Conclusion
Inthispaper,wehavestudiedN=1supersymmetricgaugetheoriesembeddedinM-theoryonlocalseven-dimensionalmanifoldswithG2holonomygroup.WehaveengineeredtheN=1quivermodelsfromG2manifolds,asU(1)quotientsofeight-dimensionaltoricHKmanifolds.Thecorrespondingquivermodelshavebeenobtainedusingareformulationofthemethodof(p,q)webs.Ourmainresultsmaybesummarizedasfollows:
(i)Usingtwo-dimensionalN=4sigma-modelswithU(1)rgaugesymmetryandr+2hy-permultiplets,wehaveconstructedaspecialkindofG2manifolds.ThelatterareU(1)quo-tientsofeight-dimensionaltoric(HK)manifolds,X7=X8
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