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

TL;DR

This work shows that a free matrix scalar field theory in the large-N limit can be mapped to bosonic string theory on AdS space with vanishing radius ($R=0$), using light-cone quantization to reveal a tensionless string with a spectrum matching multi-particle field states. Different continuum limits and σ-coordinate choices in the field theory correspond to distinct world-sheet parametrizations, while the zero-radius AdS Hamiltonian reproduces the field-theory Hamiltonian, including a mass cutoff realized as a finite warped-direction range $0<Y<Y_{max}$. The analysis demonstrates there is no critical dimension in this construction and that the spectrum is tachyon-free, with a mass term in the field theory corresponding to a hard cutoff in the warped direction, i.e., $m = 2\pi / Y_{max}$. The results suggest a framework where the large-N expansion maps to a genus expansion in a tensionless string theory, opening avenues to study interactions, confinement-like physics, and tachyon condensation in a controlled holographic setting.

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.

Figures (2)

• Figure 1: $M=4$ particles with total momentum $P_- = \sum_{n=1}^M p_-(n)$
• Figure 2: The same $M=4$ particles with total momentum $P_- = \sum_{n=1}^M p_-(n)$