- #1
Korybut
- 72
- 3
Hi there!
I have som troubles with representation theory.
It is obvious that bosonic strings fields $X^{\mu}$ has zero conformal dimension $h=0$. But when one builds Verma module (open string for example) highest weight state has the following definition
$$
L_0 \vert h \rangle = 1 \vert h \rangle
$$
All descendants states have even higher grading with respect to $L_0$. This shift is necessary for the absence or spurious states (negative norm).
How Verma module with $h=1$ coonected to open bosonic string with $h=0$?
I have som troubles with representation theory.
It is obvious that bosonic strings fields $X^{\mu}$ has zero conformal dimension $h=0$. But when one builds Verma module (open string for example) highest weight state has the following definition
$$
L_0 \vert h \rangle = 1 \vert h \rangle
$$
All descendants states have even higher grading with respect to $L_0$. This shift is necessary for the absence or spurious states (negative norm).
How Verma module with $h=1$ coonected to open bosonic string with $h=0$?