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On the K-point in moduli space

Jarod Hattab, Eran Palti, Joan Quirant

TL;DR

The paper investigates the K-point in one-parameter Calabi–Yau moduli spaces of type IIB string theory, uncovering two key features: the leading prepotential dependence on gauge couplings is exponential, and the leading gauge-kinetic terms vanish on an anti self-dual graviphoton background, aligning the K-point with conifold-like behavior rather than large complex structure. It proposes that these signals arise from integrating out an ultra-light BPS state with apparently complex charges, whose mass is doubly-exponentially small in the distance to the K-point, and analyzes this via graviphoton-background calculations and the resulting gauge-kinetic and prepotential structures. The authors demonstrate an emergent infinite-distance scenario, where the infrared physics alone drives the singularity, and discuss profound implications for the Swampland Distance Conjecture, including potential need for a milder or revised formulation. The work connects to heterotic duals, Seiberg–Witten analogies, and geometric realizations of the graviphoton background, suggesting rich, exotic IR physics at K-points and inviting further exploration of multi-parameter loci and microscopic interpretations.

Abstract

We study a class of infinite-distance loci, referred to as K-points, in one-parameter complex-structure moduli spaces of type IIB string theory compactified on Calabi-Yau manifolds. We show that around K-points the effective four-dimensional supergravity exhibits certain unusual properties. The two most prominent being that the leading order dependence of the prepotential on the gauge couplings is non-perturbative and that the leading gauge kinetic terms in the action vanish when evaluated on an anti self-dual graviphoton background. These properties are shared with the conifold locus in moduli space, rather than the large complex-structure locus. The conifold locus is well-known to arise from integrating out a charged BPS state, and so the similarities suggest that the K-point also arises from integrating out a BPS state. We develop such an interpretation, finding that it corresponds to a BPS state which is extremely light, whose mass in Planck units is doubly-exponentially small in the distance to the K-point. The state behaves as if it had complex charges, or as if it couples to the self-dual and anti self-dual parts of the graviphoton differently. Assuming such an integrating-out scenario is indeed the correct physics for the K-point, we discuss the implications for our understanding of infinite distances in moduli space and for the Swampland Distance Conjecture.

On the K-point in moduli space

TL;DR

The paper investigates the K-point in one-parameter Calabi–Yau moduli spaces of type IIB string theory, uncovering two key features: the leading prepotential dependence on gauge couplings is exponential, and the leading gauge-kinetic terms vanish on an anti self-dual graviphoton background, aligning the K-point with conifold-like behavior rather than large complex structure. It proposes that these signals arise from integrating out an ultra-light BPS state with apparently complex charges, whose mass is doubly-exponentially small in the distance to the K-point, and analyzes this via graviphoton-background calculations and the resulting gauge-kinetic and prepotential structures. The authors demonstrate an emergent infinite-distance scenario, where the infrared physics alone drives the singularity, and discuss profound implications for the Swampland Distance Conjecture, including potential need for a milder or revised formulation. The work connects to heterotic duals, Seiberg–Witten analogies, and geometric realizations of the graviphoton background, suggesting rich, exotic IR physics at K-points and inviting further exploration of multi-parameter loci and microscopic interpretations.

Abstract

We study a class of infinite-distance loci, referred to as K-points, in one-parameter complex-structure moduli spaces of type IIB string theory compactified on Calabi-Yau manifolds. We show that around K-points the effective four-dimensional supergravity exhibits certain unusual properties. The two most prominent being that the leading order dependence of the prepotential on the gauge couplings is non-perturbative and that the leading gauge kinetic terms in the action vanish when evaluated on an anti self-dual graviphoton background. These properties are shared with the conifold locus in moduli space, rather than the large complex-structure locus. The conifold locus is well-known to arise from integrating out a charged BPS state, and so the similarities suggest that the K-point also arises from integrating out a BPS state. We develop such an interpretation, finding that it corresponds to a BPS state which is extremely light, whose mass in Planck units is doubly-exponentially small in the distance to the K-point. The state behaves as if it had complex charges, or as if it couples to the self-dual and anti self-dual parts of the graviphoton differently. Assuming such an integrating-out scenario is indeed the correct physics for the K-point, we discuss the implications for our understanding of infinite distances in moduli space and for the Swampland Distance Conjecture.

Paper Structure

This paper contains 38 sections, 181 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The supergravity framework
  3. General ${\cal N}=2$ supergravity formalism
  4. The graviphoton
  5. Effective descriptions in Calabi-Yau moduli spaces
  6. Local coordinates and gauge choices
  7. The prepotential
  8. The large complex-structure region
  9. The conifold region
  10. The K-point region
  11. The gauge kinetic matrix
  12. The large complex-structure region
  13. The conifold region
  14. The K-point region
  15. Probing the theory with gauge couplings
  16. ...and 23 more sections

Figures (1)

  • Figure 1: Figure showing the moduli space of the $X_{3,3}$ Calabi-Yau, which has three singular loci. Each singular locus has a monodromy associated to it which acts on the period matrix upon circling the singular point.