Equivalence of the self-dual and Nambu-Goto strings

TL;DR

This paper demonstrates the exact equivalence between algebraic and Nambu-Goto strings in four-dimensional flat space, specifically within the self-dual or anti self-dual sectors, and discusses implications for quantization.

Contribution

It explicitly establishes the conditions under which algebraic and Nambu-Goto strings are equivalent, focusing on the self-dual sectors and their Hamiltonian formulations.

Findings

Algebraic and Nambu-Goto strings are equivalent in self-dual sectors.

The Hamiltonian formulation reveals consistent phase space structures.

Discussion on alternative quantization schemes for these strings.

Abstract

We establish explicitely the relation between the algebraic and Nambu-Goto strings when the target space is a four dimensional flat space. We find that the two theories are exactly equivalent only when the algebraic string is restricted to the self-dual or anti self-dual sectors. In its Hamiltonian formulation, the algebraic string defines a constrained system with first and second class constraints. In the self-dual case, we exhibit the appropriate set of second class constraints such that the resulting physical phase space is formulated in the same way as it is in the standard Nambu-Goto string. We conclude with a discussion on alternative quantisation schemes.