Canonical quantization of a string describing $N$ branes at angles

TL;DR

This paper develops a canonical quantization framework for bosonic strings with multiple twist fields, generalizing previous models to include non-twisted states and more than two twist fields, and computes correlators consistent with prior path integral results.

Contribution

It introduces a novel canonical quantization method for strings with multiple twist fields, including non-twisted states, and derives correlators using an improved overlap principle.

Findings

Successfully quantized strings with N twist fields at angles.

Derived the generating function for correlators with untwisted and twisted operators.

Confirmed consistency with previous path integral results.

Abstract

We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2. In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein-Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint. The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators