I have this, probably quite simple, problem. In the RNS superstring, when varying the action, we obtain in general a term [tex] \int d\tau [X'_{\mu}\delta X^{\mu}|_{\sigma=\pi}-X'_{\mu}\delta X^{\mu}|_{\sigma=0} + (\psi_+ \delta \psi_+ - \psi_- \delta \psi_-)|_{\sigma=\pi}-(\psi_+ \delta \psi_+ - \psi_- \delta \psi_-)|_{\sigma=0}][/tex], where the notation should be standard (as e.g. in Becker-Becker-Schwarz).(adsbygoogle = window.adsbygoogle || []).push({});

My question is the following: couldn't one also take other boundary conditions as those that one takes usually? For example, couldn't [tex]X^{\mu}[/tex] be anti-periodic (i.e. an antiperiodic closed string), or cuoldn't we take a boundary condition for the fermion in the form [tex]\delta \psi_+=\delta \psi_-=0[/tex]? Can one show that there are no solutions to such boundary conditions (because nobody does that in a textbook)?

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# Boundary conditions in String Theory

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