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Quantum covariant c-map

Sergei Alexandrov

Abstract

We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature.

Quantum covariant c-map

Abstract

We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature.

Paper Structure

This paper contains 15 sections, 60 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Quaternion-Kähler geometry from projective superspace
  3. Quantum c-map, hyperkäler cone and twistor space
  4. The perturbed prepotential
  5. Choice of the contour and the tensor Lagrangian
  6. Legendre transform and Kähler potential
  7. Conformal transformations and anomaly
  8. The covariant c-map
  9. Loop corrected HM moduli space
  10. The $v^{0}\to 0$ limit
  11. The quternion-Kähler metric
  12. Summary
  13. Evaluation of the tensor Lagrangian
  14. $SU(2)$ transformations
  15. Derivatives of $K_{{\cal Z}}$

Figures (1)

  • Figure 1: The singularities, logarithmic cuts and contour ${\cal C}$ on the complex $\zeta$-plane.