Novel Aspects in p-Brane Theories Weyl-Invariant Light-Like(2)

We consider a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically light-like branes for any odd world-volume dimension, hence the acronym WILL-branes (Weyl-Invariant Light-Like branes). We discuss in some detail the prop

eldanalogues,respectively.Asaresultofthelatterpropertythemodi ed-measurestringmodelwithdynamicaltensionyieldsasimpleclassicalmechanismof“color”chargecon nement.

Inthenextsectionweproceedtoourmaintaskwhichisthestudyofanovelclass( rstproposedinourprecedingwork[6])ofp-branetheorieswhichareWeyl-conformalinvariantforanypandwhichdescribeintrinsicallylight-likebranesforanyodd(p+1).Thus,theirdynamicssigni cantlydi ersbothfromthestandardNambu-Goto(orDirac-Born-Infeld)branesaswellasfromtheirmodi edversionswithdynamicalstring/branetensions[4]mentionedabove.

2

2.1Weyl-Invariantp-BraneTheoriesStandardNambu-GotoBranes

HereγabistheordinaryRiemannianmetriconthep+1-dimensionalbraneworld-volumewithγ≡det||γab||.Theworld-volumeindicesa,b=0,1,...,p;GµνdenotestheRiemannianmetricintheembeddingspace-timewithspace-timeindicesµ,ν=0,1,...,D 1.Tisthegivenadhocbranetension;theconstantΛcanbeabsorbedbyrescalingT(seebelowEq.(7)).Theequationsofmotionw.r.t.γabandXµread:

1(p 1)=0,(2)Tab≡ aXµ bXν 2

√ γγab aXν bXλΓµ a(3)νλ=0,

where:

Γµ

νλ=1Letus rstbrie yrecallthestandardPolyakov-typeformulationofthebosonicp-braneaction: TabµνS= γγ aX bXGµν(X) Λ(p 1).(1)

p+1γabγ cX dXcdµν Gµν=0.(6)

Furthermore,using(5)thePolyakov-typebraneaction(1)becomeson-shellequivalenttotheNambu-Goto-typebraneaction:

S= TΛ p 1 det|| aXµ bXνGµν||.(7)

2.2Weyl-InvariantBranes:ActionandEquationsofMotion

withFab(A)= aAb bAa,and:

Φ( )≡1Inref.[6]weproposedthefollowingnovelp-braneactions: 1p+1S= dσΦ( )Fab(A)Fcd(A)γacγbd(8)