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The DBI action, given by

$$S_{Dp}=-T_p\int d^{p+1}\xi e^{-\phi(\xi)}\sqrt{-\textrm{det}\left(G_{ab}(\xi)+B_{ab}(\xi)+2\pi{\alpha}'F_{ab}(\xi)\right)}$$

is diff and Poincaré invariant. I want to impose Weyl invariance, classically it leads to $T^{a}_{\:\:a}=0$. More directly, when I vary the action, with $\delta G^{ab}(\xi)\sim G^{ab}(\xi)$

$$\delta S_{Dp}=-T_p\int d^{p+1}\xi e^{-\phi(\xi)}\left(-\frac{1}{2}\sqrt{-M(\xi)}M_{ab}(\xi)G^{ab}(\xi)\right)=0$$

where

$$M_{ab}=G_{ab}+B_{ab}+2\pi{\alpha}'F_{ab}.$$

It produces

$$e^{-\phi(\xi)}M_{ab}(\xi)G^{ab}(\xi)=0$$

which leads to say that $\phi\rightarrow\infty$? Is it that possible? Weyl invariance should lead to some e.o.m's, not to this too strong condition.

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