Construction of bosonic string theory on infinitely curved Anti-de Sitter space

TL;DR

This paper explores how free scalar field theories with many particles can be viewed as bosonic string theories in Anti-de Sitter space with zero radius, revealing novel properties like absence of tachyons and critical dimensions.

Contribution

It establishes a new correspondence between large particle number scalar field theories and bosonic strings in a specific AdS background, including effects of mass terms and reparametrizations.

Findings

Scalar field theory maps to bosonic string theory on AdS with zero radius.

Adding mass cuts off the AdS direction, affecting the string's geometry.

The resulting string theory lacks tachyons and does not require a critical dimension.

Abstract

Free scalar field theory in the sector with a large number of particles can be interpreted as bosonic string theory on anti-de Sitter space of vanishing radius. Different ways of writing the field theory Hamiltonian translate to different ways of reparametrizing the world-sheet sigma coordinate. Adding a mass term in the field theory corresponds to cutting off the warped AdS direction, with cut-off inversely proportional to the mass. The string theory has neither tachyon, nor critical dimension.