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Duality in Heterotic Vacua With Four Supercharges

Michael Haack, Jan Louis

Abstract

We study heterotic vacua with four supercharges in three and four space-time dimensions and their duals obtained as M/F-theory compactified on Calabi-Yau fourfolds. We focus on their respective moduli spaces and derive the Kahler potential for heterotic vacua obtained as circle compactifications of four-dimensional N=1 heterotic theories. The Kahler potential of the dual theory is computed by compactifying 11-dimensional supergravity on Calabi-Yau fourfolds. The duality between these theories is checked for K3-fibred fourfolds and an appropriate F-theory limit is discussed.

Duality in Heterotic Vacua With Four Supercharges

Abstract

We study heterotic vacua with four supercharges in three and four space-time dimensions and their duals obtained as M/F-theory compactified on Calabi-Yau fourfolds. We focus on their respective moduli spaces and derive the Kahler potential for heterotic vacua obtained as circle compactifications of four-dimensional N=1 heterotic theories. The Kahler potential of the dual theory is computed by compactifying 11-dimensional supergravity on Calabi-Yau fourfolds. The duality between these theories is checked for K3-fibred fourfolds and an appropriate F-theory limit is discussed.

Paper Structure

This paper contains 13 sections, 118 equations.

Table of Contents

  1. Introduction
  2. Heterotic String Vacua
  3. $D=4, N=1$ heterotic vacua
  4. $D=4,N=1$ supergravity compactified on $S^1$
  5. The heterotic $D=3$ low energy effective Lagrangian
  6. M-theory compactified on Calabi-Yau fourfolds
  7. Duality
  8. Heterotic -- M-theory duality in $D=3$
  9. F-theory limit
  10. Conclusions
  11. Notation and conventions
  12. $S^1$ compactification of $D=4$ super-gravity
  13. Dimensional reduction of $D=11$ supergravity on Calabi-Yau fourfolds