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String loop corrected hypermultiplet moduli spaces

Daniel Robles-Llana, Frank Saueressig, Stefan Vandoren

TL;DR

The authors determine the perturbative string loop corrections to the hypermultiplet moduli space of type II strings on a generic CY$_3$, showing the HM geometry is quaternion‑Kähler and globally encoded by a single function $H(oldsymbol{ exteta})$. By employing the off‑shell superconformal tensor multiplet formalism and the c‑map, they derive a one‑loop deformation $H^{ m qc}(oldsymbol{ exteta}) = rac{F(oldsymbol{ exteta}^oldsymbol{ta})}{oldsymbol{ exteta}^0} - 4 c D(oldsymbol{ exteta}^oldsymbol{ta}) oldsymbol{ exteta}^0 oldsymbol{ta}^0 oldsymbol{}oldsymbol{ exteta}^0$ that simultaneously encodes TM and HM loop corrections, with the constants fixed by matching to known string amplitudes and parity, yielding a universal one‑loop correction proportional to the CY Euler characteristic. They further argue for a non‑renormalization theorem that higher loop corrections are absent in this perturbative sector, at least under a contour choice that encircles the origin in the auxiliary complex plane. The results generalize the universal hypermultiplet corrections and provide a controlled, symmetry‑driven framework to study perturbative corrections to HM moduli spaces, with potential implications for orientifolds, flux compactifications, and dual heterotic descriptions.

Abstract

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding quaternion-Kahler manifolds are completely encoded in terms of a single function. The latter receives a one-loop correction and, using superspace techniques, we argue for the existence of a non-renormalization theorem excluding higher loop contributions.

String loop corrected hypermultiplet moduli spaces

TL;DR

The authors determine the perturbative string loop corrections to the hypermultiplet moduli space of type II strings on a generic CY, showing the HM geometry is quaternion‑Kähler and globally encoded by a single function . By employing the off‑shell superconformal tensor multiplet formalism and the c‑map, they derive a one‑loop deformation that simultaneously encodes TM and HM loop corrections, with the constants fixed by matching to known string amplitudes and parity, yielding a universal one‑loop correction proportional to the CY Euler characteristic. They further argue for a non‑renormalization theorem that higher loop corrections are absent in this perturbative sector, at least under a contour choice that encircles the origin in the auxiliary complex plane. The results generalize the universal hypermultiplet corrections and provide a controlled, symmetry‑driven framework to study perturbative corrections to HM moduli spaces, with potential implications for orientifolds, flux compactifications, and dual heterotic descriptions.

Abstract

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding quaternion-Kahler manifolds are completely encoded in terms of a single function. The latter receives a one-loop correction and, using superspace techniques, we argue for the existence of a non-renormalization theorem excluding higher loop contributions.

Paper Structure

This paper contains 25 sections, 118 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Effective supergravity actions
  3. Tree level effective actions
  4. Off-shell formulation
  5. Tensor multiplet lagrangians
  6. The superconformal quotient for tensor multiplets
  7. The classical c-map
  8. Gauge-fixing the superconformal symmetries
  9. The tensor multiplet lagrangian
  10. The dual hypermultiplet lagrangian
  11. One-loop corrections
  12. Deformations of $H^{\rm cl}(\eta)$
  13. The deformed tensor multiplet lagrangian
  14. The deformed hypermultiplet lagrangian
  15. Matching to string loop amplitudes
  16. ...and 10 more sections

Figures (1)

  • Figure 1: Relations between the scalar manifolds featuring in the conformal (top) and Poincaré supergravity (bottom). The vertical arrows indicate that these theories are related by the superconformal quotient while the horizontal arrows imply that, provided the HM scalar manifolds have suitable isometries, scalars are dual to antisymmetric tensor fields thus relating the corresponding hyper- and tensor multiplet scalar manifolds.