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On string loops in Calabi-Yau orientifolds in large volume

Manki Kim

TL;DR

The paper develops a constructive procedure for computing string-loop amplitudes in Calabi–Yau orientifolds within the large-volume expansion using patch-by-patch superstring field theory, addressing off-shell PCO placement and degeneration limits.A concrete calculation of the D1-instanton one-loop partition function is performed to first order in the large-volume expansion, demonstrating that unphysical divergences from naive PCO choices cancel against vertical-integration boundary contributions, yielding a finite result.The work highlights that the BV master equation and partition-of-unity glueing in the patch-by-patch framework provide a systematic route to loop amplitudes in curved backgrounds and can be extended to higher orders and Ramond–Ramond flux settings.These results inform the normalization of D1-instanton amplitudes and their one-loop renormalizations of couplings, with potential applications to moduli stabilization and cosmological solutions in string theory.

Abstract

We explain and illustrate how to compute string-loop amplitudes in Calabi-Yau orientifold compactification in the large volume limit with the help of the patch-by-patch description of string field theory. We compute the one-loop partition function of the D1-instanton in type IIB string theory compactified on an O9 orientifold of a Calabi-Yau threefold to the first order in the large volume expansion. We show that the unphysical divergence arising from a naive choice of PCOs is canceled by vertical integration. The corollaries of this result, including the universal part of the normalization of the D-instanton superpotential and the one-loop renormalization of Kähler moduli, will be presented elsewhere.

On string loops in Calabi-Yau orientifolds in large volume

TL;DR

The paper develops a constructive procedure for computing string-loop amplitudes in Calabi–Yau orientifolds within the large-volume expansion using patch-by-patch superstring field theory, addressing off-shell PCO placement and degeneration limits.A concrete calculation of the D1-instanton one-loop partition function is performed to first order in the large-volume expansion, demonstrating that unphysical divergences from naive PCO choices cancel against vertical-integration boundary contributions, yielding a finite result.The work highlights that the BV master equation and partition-of-unity glueing in the patch-by-patch framework provide a systematic route to loop amplitudes in curved backgrounds and can be extended to higher orders and Ramond–Ramond flux settings.These results inform the normalization of D1-instanton amplitudes and their one-loop renormalizations of couplings, with potential applications to moduli stabilization and cosmological solutions in string theory.

Abstract

We explain and illustrate how to compute string-loop amplitudes in Calabi-Yau orientifold compactification in the large volume limit with the help of the patch-by-patch description of string field theory. We compute the one-loop partition function of the D1-instanton in type IIB string theory compactified on an O9 orientifold of a Calabi-Yau threefold to the first order in the large volume expansion. We show that the unphysical divergence arising from a naive choice of PCOs is canceled by vertical integration. The corollaries of this result, including the universal part of the normalization of the D-instanton superpotential and the one-loop renormalization of Kähler moduli, will be presented elsewhere.
Paper Structure (94 sections, 681 equations, 2 figures)

This paper contains 94 sections, 681 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Summary of the draft
  3. What this enables
  4. Non-linear sigma model in string field theory
  5. Review of string field theory
  6. Patch-by-patch description
  7. Structure of the one-loop partition function
  8. Comments on general loop amplitudes
  9. Correlation functions involving zero momentum operators
  10. Sample calculations
  11. Disk one point function
  12. Disk with C-O
  13. One-loop amplitudes at zero-th order
  14. Annulus: D1-D1
  15. Möbius
  16. ...and 79 more sections

Figures (2)

  • Figure 1: Growth of $|c_n|$
  • Figure 2: Schematic illustration of the moduli space of the Möbius strip with one closed string puncture.