- #1
synoe
- 23
- 0
The Polyakov action,
<br /> S=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-h}h^{\alpha\beta}G_{ij}(X)\partial_\alpha X^i\partial_\beta X^j<br />
has the local symmetries, diffeomorphism on world sheet and the Weyl invariance.
But is diffeomorphism on the target space also a symmetry?
The target space metric transforms
<br /> G_{ij}(X)\to G_{ij}^\prime(X^\prime)=\frac{\partial X^k}{\partial X^i}\frac{\partial X^l}{\partial X^j}G_{kl}(X).<br />
But I don't know how to deal with the part, \partial_\alpha X^i\partial_\beta X^j.
<br /> S=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-h}h^{\alpha\beta}G_{ij}(X)\partial_\alpha X^i\partial_\beta X^j<br />
has the local symmetries, diffeomorphism on world sheet and the Weyl invariance.
But is diffeomorphism on the target space also a symmetry?
The target space metric transforms
<br /> G_{ij}(X)\to G_{ij}^\prime(X^\prime)=\frac{\partial X^k}{\partial X^i}\frac{\partial X^l}{\partial X^j}G_{kl}(X).<br />
But I don't know how to deal with the part, \partial_\alpha X^i\partial_\beta X^j.