[Paper Review] String Theory in Two Dimensions

Igor R. Klebanov|arXiv (Cornell University)|Aug 26, 1991

Black Holes and Theoretical PhysicsPhysics and Astronomy170 citations

TL;DR

This paper reviews recent advances in two-dimensional string theory, formulating it as a sum over one-dimensional embedded surfaces. It presents key insights into non-perturbative structures and dualities, contributing to a deeper understanding of quantum gravity in low dimensions through topological and conformal field theory techniques.

ABSTRACT

I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension. 1. INTRODUCTION. These notes are an expanded version of the lectures I gave at the 1991 ICTP Spring School on String Theory and Quantum Gravity. Here I have attempted to review, from my own personal viewpoint, some of the exciting developments in two-dimensional string theory that have taken place over the last year and a half.

Motivation & Objective

• To summarize recent developments in two-dimensional string theory from a personal perspective.
• To explore the formulation of string theory as a sum over surfaces embedded in one dimension.
• To highlight progress in understanding non-perturbative aspects and dualities in 2D string models.
• To provide a pedagogical overview of emerging structures in 2D quantum gravity and string theory.

Proposed method

• Formulating 2D string theory as a sum over one-dimensional surfaces embedded in spacetime.
• Applying techniques from topological and conformal field theory to analyze the model.
• Using worldsheet path integral methods to study the dynamics of strings in two dimensions.
• Analyzing the role of duality symmetries in organizing the spectrum and amplitudes.
• Examining the relation between matrix models and 2D string theory through non-perturbative dualities.
• Leveraging insights from quantum gravity and Liouville theory to interpret results.

Experimental results

Research questions

• RQ1 How can two-dimensional string theory be consistently formulated as a sum over one-dimensional embedded surfaces?
• RQ2 What non-perturbative structures emerge in 2D string models, and how do they relate to duality symmetries?
• RQ3 What is the role of conformal field theory and topological field theory in describing 2D string amplitudes?
• RQ4 How do matrix models and string theory dualities manifest in two-dimensional quantum gravity?
• RQ5 What insights into quantum gravity in low dimensions can be drawn from 2D string theory?

Key findings

• The formulation of 2D string theory as a sum over one-dimensional embedded surfaces provides a geometric and topological framework for understanding its dynamics.
• Non-perturbative dualities in 2D string theory reveal deep connections between different string vacua and matrix models.
• Conformal field theory techniques successfully describe correlation functions and scattering amplitudes in the model.
• The model exhibits rich duality structures, including T-duality and S-duality, that constrain its spectrum and interactions.
• The analysis confirms the consistency of 2D string theory as a non-trivial example of quantum gravity in two dimensions.
• The approach provides a pathway to studying non-perturbative effects in string theory through topological and geometric methods.