Other String Interactions and the Possible Occurrence of Anomalies

Abstract

The construction of interactions involves finding nonlinear representations of the super-Poincaré algebra using second-quantized functional fields. For open strings it is also rather straightforward to construct the three-string interaction. The natural interaction to try is when two end points on two strings join to make one string. We start with the field representation of Chapter 7 and attempt a Hamiltonian of the form

$$ H_3 = i\int D \sum _1 D\sum _2 h(\sigma _1 ,\sigma _2 )Tr[\partial \_\Phi [\sum _1 + \sum _2 ]\Phi [\sum _1 ]\Phi [\sum _2 ]] $$

(9.1)

where the trace is taken over the SO(N) or Sp(2N) indices of the fields Φ. This time the configurations Σ₁ and Σ₂ match at two end points and we use quantities σsuch that the length of a string is πα = 2p⁺π.