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

Theequationsofmotionw.r.t.γab,u(orAa),andXµreadaccordingly:

1 γab=0,( aX bX)+γef eu fu

a

√ aχ(γ,u) √χ(γ,u)γcd( cX dX) =0,(26)(27)(28)

The rstequationaboveshowsthattheinducedmetricgab≡( aX bX)haszero-modeeigenvectorVa=γab bu.

Theinvarianceunderworld-volumereparametrizationsallowstointroducethefollowingstandard(synchronous)gauge- xingconditions:

γ0i=0(i=1,2),γ00= 1.(29) γγab aXν bXλΓµνλ=0.

Inspiteofthehighnon-linearityofEq.(27)forthedual“gaugepotential”u,wecaneasily ndsolutionsbyusingthefollowingansatz:

u(τ,σ1,σ2)=T0τ,2(30)

whereT0isanarbitraryintegrationconstantwiththedimensionofmembranetension.Inparticular:

χ≡

(33)2

NotethatEqs.(33)lookexactlyliketheclassical(Virasoro)constraintsforanEuclideanstringtheorywithworld-sheetparameters(σ1,σ2).

Thegaugechoicefor(29)togetherwiththeansatz(30),aswellastakingintoaccount(32),bringthetheequationsofmotionw.r.t.utotheform:

√ 0γijγkl( kX lX)=0,

γ(2) 0 +1

γ(2) i