Other String Interactions and the Possible Occurrence of Anomalies
Part of the Series of the Centro de Estudios Científicos de Santiago book series (SCEC)
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
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.
$$ H_3 = i\int D \sum _1 D\sum _2 h(\sigma _1 ,\sigma _2 )Tr[\partial \_\Phi [\sum _1 + \sum _2 ]\Phi [\sum _1 ]\Phi [\sum _2 ]] $$
Unable to display preview. Download preview PDF.
© Plenum Press, New York 1988