User:Dimension10/Workspace

I do not guarantee the accuracy of these articles, as they may be incomplete, e.g. $$\mathcal L = -T $$ where I have not put the integral of the unknown action yet ($$ T $$ is the Tension.). .

Currently editing:  GS string theory

=GS string theory=

GS string theory, or the GS superstring theory was an early attempt to include fermions in string theory. "GS" stands for Green-Schwarz. In contrast to the RNS string theory, the GS string theory automatically has spacetime supersymmetry, but not worldsheet supersymmetry.

Action Principle
The GS string theory is determined by the Action :

$$

S = -\frac{1}{4\pi}\int \mbox{d} ^2 \xi  \sqrt{-h}h^{\alpha\beta}\partial_{\alpha}X^{\mu}\partial_{\beta}X_{\mu} -\frac{1}{4 \pi}\int \mbox{d}^2  \xi  \sqrt{-h}h^{\alpha\beta}\Pi_{\alpha}^{\mu}\Pi_{\beta} ^{\mu}  $$

Where $$  \Pi_\alpha^\mu = \partial_\alpha X^\mu - i\bar{\psi^\nu} \gamma^\mu \psi^\nu      $$   is the "real" fermionic field on spacetime as opposed to the fermionic field in RNS string theory, which is interpreted as a spacetime vector.

This is actually the worldsheet action, and an interesting thing to note is that this does not include an additional term, which arises through the kappa symmetry, which is the following term:.