String in Horava-Lifshitz Gravity

TL;DR

This paper extends the analysis of point particles in Horava-Lifshitz gravity to strings, deriving a Lorentz-violating string theory invariant under foliation-preserving diffeomorphisms with well-defined Hamiltonian dynamics.

Contribution

It introduces a Lorentz-violating string model in Horava-Lifshitz background and analyzes its symmetries and Hamiltonian structure.

Findings

The world-sheet theory is invariant under foliation-preserving diffeomorphisms.

The Hamiltonian dynamics is well-defined under the projectability condition.

The model generalizes point particle dynamics to string probes in Horava-Lifshitz gravity.

Abstract

We generalize recent analysis of the dynamics of point particle in Horava-Lifshitz background to the case of string probe when we replace the Hamiltonian constraint of the Polyakov string with the constraint that breaks Lorentz invariance of target space-time. Then we find corresponding Lagrangian and argue that the world-sheet theory is invariant under foliation preserving diffeomorphism. Finally we discuss the Hamiltonian dynamics and show that this is well defined on condition that the world-sheet lapse function obeys the projectability condition.