Bosonic string theory with constraints linear in the momenta

TL;DR

This paper reviews the Hamiltonian analysis of bosonic string theory, focusing on gauge invariance and introduces new gauge-invariant formulations with actions linear in momenta, including tensionless strings.

Contribution

It presents a method to achieve fully gauge-invariant actions for string theories, including tensionless strings, by adding boundary terms and canonical transformations.

Findings

Boundary terms restore gauge invariance of the Hamiltonian action.

A gauge-invariant formulation with linear momentum dependence is constructed for tensionless strings.

Pure diffeomorphism string theory is identified as a sub-sector of solutions.

Abstract

The Hamiltonian analysis of Polyakov action is reviewed putting emphasis in two topics: Dirac observables and gauge conditions. In the case of the closed string it is computed the change of its action induced by the gauge transformation coming from the first class constraints. As expected, the Hamiltonian action is not gauge invariant due to the Hamiltonian constraint quadratic in the momenta. However, it is possible to add a boundary term to the original action to build a fully gauge-invariant action at first order. In addition, two relatives of string theory whose actions are fully gauge-invariant under the gauge symmetry involved when the spatial slice is closed are built. The first one is pure diffeomorphism in the sense it has no Hamiltonian constraint and thus bosonic string theory becomes a sub-sector of its space of solutions. The second one is associated with the tensionless bosonic string, its boundary term induces a canonical transformation and the fully gauge-invariant action written in terms of the new canonical variables becomes linear in the momenta.