Boundary conditions for open and closed strings

[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: [itex]\psi^+(\sigma = \pi, t) = \psi^-(\sigma = \pi, t)[/itex]
Neveu-Schwarz case: [itex]\psi^+(\sigma = \pi, t) = -\psi^-(\sigma = \pi, t)[/itex]

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: [itex]\psi^+(\sigma = 0) = \psi^+(\sigma = \pi)[/itex], [itex]\psi^+(\sigma = 0) = \psi^-(\sigma = \pi)[/itex]

Neveu-Schwarz case: [itex]\psi^+(\sigma = 0) = \psi^+(\sigma = \pi)[/itex], [itex]\psi^+(\sigma = 0) = -\psi^-(\sigma = \pi)[/itex]

Question 2: So,

NS-NS means both [itex]\psi^+[/itex] and [itex]\psi^-[/itex] are antiperiodic
NS-R means [itex]\psi^+[/itex] is antiperiodic and [itex]\psi^-[/itex] is periodic
R-NS means [itex]\psi^-[/itex] is antiperiodic and [itex]\psi^+[/itex] is periodic
R-R means [itex]\psi^+[/itex] is periodic and [itex]\psi^-[/itex] 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.

 

[AndyW]

Thank you for your questions regarding the terminology used for the boundary conditions of open and closed strings. I will do my best to clarify these concepts for you.

To answer your first question, yes, you are correct in your understanding that the "R sector" refers to the Ramond case and the "NS sector" refers to the Neveu-Schwarz case. These terms come from the names of the physicists who first proposed these boundary conditions, Pierre Ramond and John Neveu-Schwarz.

For your second question, you are also correct in your understanding of the different sectors for closed strings. NS-NS means that both \psi^+ and \psi^- are antiperiodic, which means they have a half-integer multiple of the fundamental frequency. NS-R means that \psi^+ is antiperiodic and \psi^- is periodic, while R-NS means that \psi^- is antiperiodic and \psi^+ is periodic. Finally, R-R means that both \psi^+ and \psi^- are periodic, meaning they have an integer multiple of the fundamental frequency.

I understand that these concepts can be confusing, but it is important to note that these boundary conditions are necessary in order to satisfy the equations of motion for the strings. The different sectors arise from the different ways in which the strings can vibrate and interact with each other.

I hope this helps to clarify the terminology and concepts for you. If you have any further questions, please do not hesitate to ask.