The Power of Worldsheets: Applications and Prospects

TL;DR

This paper explores the worldsheet formulation of string theory, demonstrating its renormalizability and finiteness, and investigates nonperturbative states, solitons, and thermodynamics, including phase transitions and stability of string gases.

Contribution

It provides a detailed worldsheet perspective on string theory's finiteness, nonperturbative states, and thermodynamic behavior, including phase transitions and stability analysis.

Findings

String scattering amplitudes are finite and unambiguously normalized.

The Hagedorn phase transition is absent in free closed string gases.

Stable finite temperature ground state for heterotic strings with SO(16)xSO(16) gauge group.

Abstract

We explain how perturbative string theory can be viewed as an exactly renormalizable Weyl invariant quantum mechanics in the worldsheet representation clarifying why string scattering amplitudes are both finite and unambiguously normalized and explaining the origin of UV-IR relations in spacetime. As applications we examine the worldsheet representation of nonperturbative type IB states and of string solitons. We conclude with an analysis of the thermodynamics of a free closed string gas establishing the absence of the Hagedorn phase transition. We show that the 10D heterotic strings share a stable finite temperature ground state with gauge group SO(16)xSO(16). The free energy at the self-dual Kosterlitz-Thouless phase transition is minimized with finite entropy and positive specific heat. The open and closed string gas transitions to a confining long string phase at a temperature at or below the string scale in the presence of an external electric field.