Novel Aspects in p-Brane Theories Weyl-Invariant Light-Like(6)

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

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4.1WILL-MemraneSolutionsinNon-TrivialGravitationalBack-groundsExample:WILL-MembraneinSpherically-SymmetricStaticBackgroundsLetusconsiderageneralspherically-symmetricstaticgravitationalbackgroundinD=4embeddingspace-time:

(ds)2= A(r)(dt)2+B(r)(dr)2+r2[(dθ)2+sin2(θ)(dφ)2].(37)

Speci callywehave:

A(r)=B 1(r)=1 2GM

r+Q2

τ

τrr=±A(r), =0whichuponcombiningwith(43)gives:

r=r0≡const,whereA(r0)=0.(44)

TheX0-equationofmotion(Eq.(35)forµ=0)impliesfortheintrinsicWILL-membranemetric:

10,(45) γij =c0e τ/r00sin2(σ1)

wherec0isanarbitraryintegrationconstant.

From(44)weconcludethattheWILL-membranewithsphericaltopology(andwithexponentiallyblowing-up/de atingradiusw.r.t.internalmetric)“sits”on(materializes)theeventhorizonofthepertinentblackholeinD=4embeddingspace-time.

4.2Example:WILL-membraneinProduct-SpaceBackgrounds

HereweconsiderWILL-membranemovinginageneralproduct-spaceD=(d+2)-dimensionalgravi-tationalbackgroundMd×Σ2withcoordinates(xµ,ym)(µ=0,1,...,d 1,m=1,2)andRiemannianmetric(ds)2=f(y)gµν(x)dxµdxν+gmn(y)dymdyn.

WeassumethattheWILL-branewrapsaroundthe“internal”spaceΣ2andusethefollowingansatz(recallτ≡σ0):

Xµ=Xµ(τ),Ym=σm,γmn=a(τ)gmn(σ1,σ2)(46)

Thentheequationsofmotionandconstraints(32)–(36)reduceto:

τXµ τXνgµν(X)=0,1