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A Large-N Reduced Model as Superstring

N. Ishibashi, H. Kawai, Y. Kitazawa, A. Tsuchiya

TL;DR

The authors propose a large-N reduced matrix model of ten-dimensional N=2 super Yang–Mills as a constructive definition of type IIB string theory, with a Schild-gauge Green–Schwarz mapping and clear SUSY structure. One-loop analyses around BPS backgrounds show massless spectra and D-string interactions consistent with type IIB string theory, while diagonal-block dynamics reveal a cluster property and space-time generation from collective coordinates. They establish a double-scaling limit linking the matrix model to the underlying SYM theory, identify a chemical-potential term from zero modes, and discuss renormalization and the continuum limit as a nonperturbative definition. The work argues for dual interpretations across moduli space (IIB vs. IIA) and posits a nonperturbative, unified framework for string theory via large-N reduced models. Overall, it provides evidence that the reduced model captures key string-theoretic features and offers a potential constructive formulation of type IIB string theory.

Abstract

A matrix model which has the manifest ten-dimensional N=2 super Poincare invariance is proposed. Interactions between BPS-saturated states are analyzed to show that massless spectrum is the same as that of type IIB string theory. It is conjectured that the large-N reduced model of ten-dimensional super Yang-Mills theory can be regarded as a constructive definition of this model and therefore is equivalent to superstring theory.

A Large-N Reduced Model as Superstring

TL;DR

The authors propose a large-N reduced matrix model of ten-dimensional N=2 super Yang–Mills as a constructive definition of type IIB string theory, with a Schild-gauge Green–Schwarz mapping and clear SUSY structure. One-loop analyses around BPS backgrounds show massless spectra and D-string interactions consistent with type IIB string theory, while diagonal-block dynamics reveal a cluster property and space-time generation from collective coordinates. They establish a double-scaling limit linking the matrix model to the underlying SYM theory, identify a chemical-potential term from zero modes, and discuss renormalization and the continuum limit as a nonperturbative definition. The work argues for dual interpretations across moduli space (IIB vs. IIA) and posits a nonperturbative, unified framework for string theory via large-N reduced models. Overall, it provides evidence that the reduced model captures key string-theoretic features and offers a potential constructive formulation of type IIB string theory.

Abstract

A matrix model which has the manifest ten-dimensional N=2 super Poincare invariance is proposed. Interactions between BPS-saturated states are analyzed to show that massless spectrum is the same as that of type IIB string theory. It is conjectured that the large-N reduced model of ten-dimensional super Yang-Mills theory can be regarded as a constructive definition of this model and therefore is equivalent to superstring theory.

Paper Structure

This paper contains 13 sections, 132 equations.

Table of Contents

  1. Introduction
  2. Relations between Green-Schwarz superstring and a matrix model
  3. One-loop quantum corrections around classical solutions
  4. Classical static D-string solutions
  5. One-loop effective action and stability of BPS-saturated states
  6. Interactions between two static D-strings
  7. Interactions between diagonal blocks and cluster property
  8. Determination of $\alpha$ and $\beta$
  9. The large-N reduced model of super Yang-Mills theory
  10. Double scaling limit
  11. Generation of the chemical potential term and one-loop renormalization
  12. Moduli space of the matrix model
  13. Summary and discussion