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

[28]Y.-H.He,G2Quivers,JHEP0302(2003)023,hep-th/0210127.

[29]J.McKay,Graphs,Singularities,andFiniteGroups,ProcSymp.Pure.Math.Vo37

(1980)183.

[30]A.Belhaj,ManifoldsofG2HolonomyfromN=4SigmaModel,J.Phys.A35(2002)8903,

hep-th/0201155.

[31]W.Fulton,IntroductiontoToricvarieties,AnnalsofMath.Studies,No.131,Princeton

UniversityPress,1993.

[32]N.C.LeungandC.Vafa,Adv.Theor.Math.Phys.2(1998)91,hep-th/9711013.

[33]D.Cox,Thehomogeneouscoordinateringofatoricvariety,J.Alg.geom.4(1995)17.

[34]M.Kreuzer,H.Skarke,Re exivepolyhedra,weightsandtoricCalabi-Yau brations,

math.AG/0001106.

A.C.Avram,M.Kreuzer,M.Mandelberg,H.Skarke,ThewebofCalabi-Yauhypersur-facesintoricvarieties,Nucl.Phys.B505(1997)625,hep-th/9703003.

M.Kreuzer,H.Skarke,Calabi-Yau4-foldsandtoric brations,J.Geom.Phys.26(1998)272,hep-th/9701175.

[35]E.Witten,Nucl.Phys.B403(1993)159,hep-th/9301042.

[36]A.Belhaj,E.H.Saidi,Hyper-K¨ahlerSingularitiesinSuperstringsCompacti cation

and2dN=4ConformalFieldTheory,ClassicalQuantumGgravity,18(2001)57,hep-th/0002205.

A.Belhaj,E.H.Saidi,OnHyper-K¨ahlerSingularities;Mod.Phys.Lett.A,Vol.15,No.29(2000)1767,hep-th/0007143.

[37]K.Hori,C.Vafa,MirrorSymmetry,hep-th/0002222.

[38]K.Hori,A.Iqbal,C.Vafa,D-BranesAndMirrorSymmetry,hep-th/0005247.

[39]M.Aganagic,C.Vafa,MirrorSymmetry,D-branesandCountingHolomorphicDiscs,

hep-th/0012041.

M.Aganagic,C.Vafa,MirrorSymmetryandG2Flop,hep-th/0105225.

M.Aganagic,A.Klemm,C.Vafa,DiskInstantons,MirrorSymmetryandtheDualityWeb,hep-th/0105045.