Problem 14.5c5

Counting states in heterotic SO(32) string theory | A First Course in String Theory


c) Are there tachyonic states in heterotic string theory?

Write out the massless states of the theory (bosons and fermions) …



We have the following well-known bosonic string mass formulae:

open string:

\displaystyle{\alpha' M^2 = N - a}

closed string:

\displaystyle{\frac{1}{4} \alpha' M^2 = N_L - a}
\displaystyle{\frac{1}{4} \alpha' M^2 = N_R - a}


— Solutions to K. Becker, M. Becker, J. Schwarz String Theory And M-theory

— Mikhail Goykhman


How come there is an extra \displaystyle{\frac{1}{4}} at the beginning of the closed string formula?


\displaystyle{\frac{1}{2} \alpha' M^2 = \alpha' M_L^2 + \alpha' M_R^2}


\displaystyle{\begin{aligned}  \alpha' M_L^2 &= \alpha' M_R^2 \\  \frac{1}{2} \alpha' M^2 &= \alpha' M_L^2 + \alpha' M_R^2 \\  \alpha' M^2 &= 2 \left( \alpha' M_L^2 + \alpha' M_R^2 \right) = 4 \alpha' M_L^2 \\  \end{aligned}}

— Me@2018-12-15 08:59:18 PM



2018.12.15 Saturday (c) All rights reserved by ACHK