Problem 14.3b1

A First Course in String Theory

14.3 Massive level in the open superstring.

~~~

What is the difference between “open bosonic string” and “open superstring”?

p.320 “With our conventions, these are world-sheet fermionic states that are now recognized to be states of spacetime fermions. The resulting, truncated sector is called the R- sector.”

NS(+): Equation (14.38) $\left(\alpha' M^2 = 1, N^\perp = \frac{3}{2}\right)$ :

$\left\{ \alpha_{-1}^I b_{-1/2}^J, b_{-3/2}^I, b^I_{-1/2} b^J_{-1/2} b^K_{-1/2} \right\} | NS \rangle \otimes | p^+, \vec p_R \rangle$

There are 128 states (cf. Quick Calculation 14.4).

R: Equation (14.54) $\left(\alpha' M^2 = 1\right)$ :

$\alpha^I_{-1} | R_a \rangle, d_{-1}^I | R_{\bar a} \rangle~||~\alpha^I_{-1} | R_{\bar a} \rangle, d_{-1}^I | R_{a} \rangle$

Only the left hand side represents the R- states.

Each of index $I$ and index $a$ has 8 possible values. So there are totally 64 states in the form of $\alpha^I_{-1} | R_a \rangle$ .

Similarly, there are totally 64 states in the form of $d_{-1}^I | R_{\bar a} \rangle$ .

Totally, for $\alpha' M^2 = 1$ , there are 128 R- states.

Physics Town

continues

Problem 14.3b1

Related