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A Heterotic Kähler Gravity and the Distance Conjecture

Javier José Murgas Ibarra, Paul-Konstantin Oehlmann, Fabian Ruehle, Eirik Eik Svanes

TL;DR

This work builds a heterotic Kodaira–Spencer–type theory from fluctuations of the heterotic superpotential, revealing a cubic but effectively quadratic action in the Beltrami differential that, at large flux or large complex-structure distance, can be integrated to a topological theory for the remaining Hermitian and gauge modes. It demonstrates two distinct towers of light states arising in the infinite-distance limit, consistent with the swampland Distance Conjecture, and connects these physics insights to a new elliptic, symplectic-type cohomology structure governed by the background Beltrami differential. The paper also develops a SYZ-inspired three-dimensional toy model to study dimensional reduction and provides several gauge-coupled extensions, including a discussion of gauge fields via $\alpha'$ corrections and potential implications for Donaldson–Thomas theory and BV quantization. Overall, the work links geometric moduli, flux backgrounds, and quantum gravity constraints in the heterotic setting, and lays groundwork for further mathematical and physical exploration of these novel effective actions and their infinite-distance behavior.

Abstract

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form.

A Heterotic Kähler Gravity and the Distance Conjecture

TL;DR

This work builds a heterotic Kodaira–Spencer–type theory from fluctuations of the heterotic superpotential, revealing a cubic but effectively quadratic action in the Beltrami differential that, at large flux or large complex-structure distance, can be integrated to a topological theory for the remaining Hermitian and gauge modes. It demonstrates two distinct towers of light states arising in the infinite-distance limit, consistent with the swampland Distance Conjecture, and connects these physics insights to a new elliptic, symplectic-type cohomology structure governed by the background Beltrami differential. The paper also develops a SYZ-inspired three-dimensional toy model to study dimensional reduction and provides several gauge-coupled extensions, including a discussion of gauge fields via corrections and potential implications for Donaldson–Thomas theory and BV quantization. Overall, the work links geometric moduli, flux backgrounds, and quantum gravity constraints in the heterotic setting, and lays groundwork for further mathematical and physical exploration of these novel effective actions and their infinite-distance behavior.

Abstract

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form.
Paper Structure (20 sections, 211 equations)

This paper contains 20 sections, 211 equations.

Table of Contents

  1. Introduction
  2. The Distance Conjecture
  3. The Heterotic Effective Action
  4. The Effective Action
  5. Heterotic action including the dilaton
  6. Integrating out the dilaton from the exact action
  7. Infinite Distance Limits
  8. Elliptic complexes and symplectic cohomology
  9. The first term of the dilaton effective action
  10. The second term of the dilaton effective action
  11. The full dilaton effective action
  12. The SYZ fibration and a three-dimensional toy model
  13. The model
  14. An alternative model
  15. Including gauge fields
  16. ...and 5 more sections

Theorems & Definitions (2)

  • proof
  • proof