Open & Closed vs. Pure Open String Disk Amplitudes

Understand

We establish a relation between disk amplitudes involving N_o open and N_c closed strings and disk amplitudes with only N_o+2N_c open strings.

• This map, which represents a sort of generalized KLT relation on the disk, reveals important structures between open & closed and pure open string disk amplitudes: it relates couplings of brane and bulk string states to pure brane couplings.
• On the string world-sheet this becomes a non-trivial monodromy problem, which reduces the disk amplitude of N_o open and N_c closed strings to a sum of many color ordered partial subamplitudes of N_o+2N_c open strings.
• This sum can be further reduced to a sum over (N_o+2N_c-3)! subamplitudes of N=N_o+2N_c open strings only.