# Boundary conditions for open and closed strings

1. Sep 17, 2014

### maverick280857

Hi,

I am a bit confused about the terminology used for the boundary conditions describing open and closed strings.

For the open string,

Ramond case: $\psi^+(\sigma = \pi, t) = \psi^-(\sigma = \pi, t)$
Neveu-Schwarz case: $\psi^+(\sigma = \pi, t) = -\psi^-(\sigma = \pi, t)$

Question 1: Is it correct that the "R sector" refers to the Ramond case, and the "NS sector" refers to the Neveu-Schwarz case?

For the closed string,

Ramond case: $\psi^+(\sigma = 0) = \psi^+(\sigma = \pi)$, $\psi^+(\sigma = 0) = \psi^-(\sigma = \pi)$

Neveu-Schwarz case: $\psi^+(\sigma = 0) = \psi^+(\sigma = \pi)$, $\psi^+(\sigma = 0) = -\psi^-(\sigma = \pi)$

Question 2: So,

NS-NS means both $\psi^+$ and $\psi^-$ are antiperiodic
NS-R means $\psi^+$ is antiperiodic and $\psi^-$ is periodic
R-NS means $\psi^-$ is antiperiodic and $\psi^+$ is periodic
R-R means $\psi^+$ is periodic and $\psi^-$ is periodic?

I apologize for the triviality of these questions but the classification of the 4 sectors is confusing me a little...

I'd appreciate some help.