- #1
synoe
- 23
- 0
In string theory, the Neveu-Schwarz B-field appears in the action:
<br /> S_{NS}=\frac{1}{4\pi\alpha^\prime}\int d^2\xi\;\epsilon^{\mu\nu}B_{ij}\partial_\mu X^i\partial_\nu X^j.<br />
In Polchinski's text, the antisymmetric tensor appears in the form of
<br /> \frac{1}{4\pi\alpha^\prime}\int d^2\xi\;\sqrt{\gamma}i\epsilon^{\mu\nu}B_{ij}\partial_\mu X^i\partial_\nu X^j,<br />
where \gamma is the world sheet metric.
(1)
These terms are same?
Terms apparently these terms seem to be called NS-NS 2-form, Wess-Zumino-Witten term, or just antisymmeteric tensor. These terminologies are the same meaning?
(2)
What's the definition of \epsilon^{\mu\nu}?
(3)
Is this term conformal invariant?
Could you show the invariance?
<br /> S_{NS}=\frac{1}{4\pi\alpha^\prime}\int d^2\xi\;\epsilon^{\mu\nu}B_{ij}\partial_\mu X^i\partial_\nu X^j.<br />
In Polchinski's text, the antisymmetric tensor appears in the form of
<br /> \frac{1}{4\pi\alpha^\prime}\int d^2\xi\;\sqrt{\gamma}i\epsilon^{\mu\nu}B_{ij}\partial_\mu X^i\partial_\nu X^j,<br />
where \gamma is the world sheet metric.
(1)
These terms are same?
Terms apparently these terms seem to be called NS-NS 2-form, Wess-Zumino-Witten term, or just antisymmeteric tensor. These terminologies are the same meaning?
(2)
What's the definition of \epsilon^{\mu\nu}?
(3)
Is this term conformal invariant?
Could you show the invariance?
