Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Strong-Weak Coupling Duality in Four Dimensional String Theory

Ashoke Sen

TL;DR

This work provides evidence for a non-perturbative S-duality in four-dimensional heterotic string theory compactified on T^6, revealing an SL(2,Z) symmetry that exchanges electric string states with magnetic solitons. The approach unifies the low-energy action, the electric/magnetic charge lattice, and the Bogomol'nyi-bound mass spectrum under SL(2,Z), while contrasting with the perturbative O(6,22;Z) T-duality. It also connects S-duality to a target-space duality in the five-brane theory, suggesting a broader 'duality of dualities' framework and predicting a host of new BPS dyons and monopoles whose existence hinges on the global SL(2,Z) invariance. The paper outlines concrete open problems, including explicit constructions of the predicted states and a fuller five-brane interpretation, to solidify S-duality as a fundamental symmetry of the theory.

Abstract

We present several pieces of evidence for strong-weak coupling duality symmetry in the heterotic string theory, compactified on a six dimensional torus. These include symmetry of the 1) low energy effective action, 2) allowed spectrum of electric and magnetic charges in the theory, 3) allowed mass spectrum of particles saturating the Bogomol'nyi bound, and 4) Yukawa couplings between massless neutral particles and massive charged particles saturating the Bogomol'nyi bound. This duality transformation exchanges the electrically charged elementary string excitations with the magnetically charged soliton states in the theory. It is shown that the existence of a strong-weak coupling duality symmetry in four dimensional string theory makes definite prediction about the existence of new stable monopole and dyon states in the theory with specific degeneracies, including certain supersymmetric bound states of monopoles and dyons. The relationship between strong-weak coupling duality transformation in string theory and target space duality transformation in the five-brane theory is also discussed. (Based on a talk given at the workshop on Strings and Gravity, Madras, India.)

Strong-Weak Coupling Duality in Four Dimensional String Theory

TL;DR

This work provides evidence for a non-perturbative S-duality in four-dimensional heterotic string theory compactified on T^6, revealing an SL(2,Z) symmetry that exchanges electric string states with magnetic solitons. The approach unifies the low-energy action, the electric/magnetic charge lattice, and the Bogomol'nyi-bound mass spectrum under SL(2,Z), while contrasting with the perturbative O(6,22;Z) T-duality. It also connects S-duality to a target-space duality in the five-brane theory, suggesting a broader 'duality of dualities' framework and predicting a host of new BPS dyons and monopoles whose existence hinges on the global SL(2,Z) invariance. The paper outlines concrete open problems, including explicit constructions of the predicted states and a fuller five-brane interpretation, to solidify S-duality as a fundamental symmetry of the theory.

Abstract

We present several pieces of evidence for strong-weak coupling duality symmetry in the heterotic string theory, compactified on a six dimensional torus. These include symmetry of the 1) low energy effective action, 2) allowed spectrum of electric and magnetic charges in the theory, 3) allowed mass spectrum of particles saturating the Bogomol'nyi bound, and 4) Yukawa couplings between massless neutral particles and massive charged particles saturating the Bogomol'nyi bound. This duality transformation exchanges the electrically charged elementary string excitations with the magnetically charged soliton states in the theory. It is shown that the existence of a strong-weak coupling duality symmetry in four dimensional string theory makes definite prediction about the existence of new stable monopole and dyon states in the theory with specific degeneracies, including certain supersymmetric bound states of monopoles and dyons. The relationship between strong-weak coupling duality transformation in string theory and target space duality transformation in the five-brane theory is also discussed. (Based on a talk given at the workshop on Strings and Gravity, Madras, India.)

Paper Structure

This paper contains 21 sections, 132 equations.

Table of Contents

  1. Introduction
  2. Symmetry of the Effective Action
  3. Dimensional Reduction of the Ten Dimensional Theory
  4. O(6,22) and SL(2,R) Symmetries of the Effective Field Theory
  5. Manifestly SL(2,R) Invariant Action
  6. Manifestly SL(2,R) Invariant Effective Action from Dimensional Reduction of the Dual $N=1$ Supergravity Theory in Ten Dimensions
  7. Inclusion of the Fermions
  8. Symmetry of the Charge Spectrum
  9. Breaking of SL(2,R) to SL(2,Z)
  10. SL(2,Z) Invariance of the Electric and Magnetic Charge Spectrum
  11. Symmetry of the Mass Spectrum
  12. Symmetry of the Yukawa Couplings
  13. Where are the SL(2,Z) Transform of the Elementary String Excitations?
  14. Where Do the Known Elementary String Excitations Fit in?
  15. Where Do the Known Solitons Fit in?
  16. ...and 6 more sections