Covariant Closed String Bits -- Classical Theory

TL;DR

This paper develops a lattice formulation of covariant closed string theory with continuous time, preserving continuum symmetries and classical algebras, enabling analysis of string bits in a discretized setting.

Contribution

It introduces a non-local lattice derivative that maintains all continuum symmetries, including local worldsheet symmetries, and demonstrates the classical Virasoro algebra on the lattice.

Findings

Preserves continuum symmetries on the lattice.

Establishes classical Virasoro algebra in position space.

Provides a framework for higher-dimensional covariant theories.

Abstract

We study lattice wouldsheet theory with continuous time describing free motion of a system of bound string bits. We use a non-local lattice derivative that allows us to preserve all the symmetries of the continuum including the worldsheet local symmetries. There exists a ``local correspondence'' between the continuum and lattice theories in the sense that every local dynamical or constraint equation in the continuum also holds true on the lattice, site-wise. We perform a detailed symmetry analysis for the bits and establish conservation laws. In particular, for a bosonic non-linear sigma model with arbitrary target space, we demonstrate both the global symmetry algebra and classical Virasoro algebra (in position space) on the lattice. Our construction is generalizable to higher dimensions for any generally covariant theory that can be studied by expanding around a globally hyperbolic spacetime with conformally flat Cauchy slices.