Novel Aspects in p-Brane Theories Weyl-Invariant Light-Like(4)

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

ontheworld-volumeoftheWeyl-invariantbrane(8)issingularasopposedtotheordinaryNambu-GotobranewheretheinducedmetricisproportionaltotheintrinsicRiemannianworld-volumemetric(cf.Eq.(5)).Inotherwords:

( aX bX)Vb=0,i.e.( VX VX)=0,( ⊥X VX)=0,(17)

where V≡Va aand ⊥arederivatesalongthetangentvectorsinthecomplementofthetangentvector eldVa.

Theconstraints(17)implythefollowingimportantconclusion:everypointonthe( xed-time)world-surfaceoftheWeyl-invariantp-brane(8)(forodd(p+1))movesinorthogonaldirectionw.r.t.itselfwiththespeedoflightinatime-evolutionalongthezero-eigenvaluevector- eldVaoftheworld-volumeelectromagnetic eld-strengthFab.Therefore,wewillcall(8)(forodd(p+1))bytheacronymWILL-brane(Weyl-InvariantLight-Like-brane)model.

2.4DualFormulationofWILL-Branes

TheAa-equationsofmotion(14)canbesolvedintermsof(p 2)-formgaugepotentialsΛa1...ap 2dualw.r.t.Aa.Therespective eld-strengthsarerelatedasfollows:

Fab(A)= 1 γεabc1...cp 1

√

(p 1)2γa1b1...γap 1bp 1Fa1...ap 1(Λ)Fb1...bp 1(Λ).(20)

Now,theBiancchiidentitiesforAaturnintodynamicalequationsofmotionforthedual(p 2)-formgaugepotentialsΛa1...ap 2:

√ a(21)γabγa1b1...γap 2bp 2Fbb1...bp 2(Λ)γcd( cX dX)=0χ(γ,Λ)

Allequationsofmotion(13),(15)and(21)canbeequivalentlyderivedfromthefollowingdualWILL-braneaction:1Sdual= γγab aXµ bXνGµν(22)withχ(γ,Λ)givenin(20)above.

3TheWILL-Membrane

1 γγab( aX bX),

χ(γ,u)≡

√TheWILL-membranedualaction(particularcaseof(22)forp=2)reads:Sdual= (23)2χ(γ,u)