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Multi-instanton and string loop corrections in toroidal orbifold models

P. G. Camara, E. Dudas

TL;DR

This work analyzes $ abla^2$-sector corrections in Type I toroidal orbifolds with heterotic duals, deriving multi-instanton and one-loop string corrections to the Kahler potential $K$ and gauge kinetic functions $f_a$ for two explicit models (BSGP and a freely-acting $\,\mathbb{Z}_2\times\mathbb{Z}_2\,$). By matching heterotic one-loop gauge couplings, the authors express non-perturbative corrections as sums over Hecke operators and recover known one-loop Kahler corrections, highlighting a universal structure tied to target-space modular invariance (or its subgroup) across models. They provide explicit partition functions and unfolding techniques that map threshold integrals to modular-invariant sums, including $\,\Gamma_0(2)\,$ automorphic forms in the freely-acting case. The results illuminate how $ abla^2$ corrections shape low-energy couplings and moduli stabilization prospects, and point toward broader universality and applications in other ${\cal N}=2$ and ${\cal N}=1$ orbifolds through duality and automorphic methods.

Abstract

We analyze N=2 (perturbative and non-perturbative) corrections to the effective theory in type I orbifold models where a dual heterotic description is available. These corrections may play an important role in phenomenological scenarios. More precisely, we consider two particular compactifications: the Bianchi-Sagnotti-Gimon-Polchinski orbifold and a freely-acting Z_2 x Z_2 orbifold with N=1 supersymmetry and gauge group SO(q) x SO(32-q). By exploiting perturbative calculations of the physical gauge couplings on the heterotic side, we obtain multi-instanton and one-loop string corrections to the Kähler potential and the gauge kinetic function for these models. The non-perturbative corrections appear as sums over relevant Hecke operators, whereas the one-loop correction to the Kähler potential matches the expression proposed in [1,2]. We argue that these corrections are universal in a given class of models where target-space modular invariance (or a subgroup of it) holds.

Multi-instanton and string loop corrections in toroidal orbifold models

TL;DR

This work analyzes -sector corrections in Type I toroidal orbifolds with heterotic duals, deriving multi-instanton and one-loop string corrections to the Kahler potential and gauge kinetic functions for two explicit models (BSGP and a freely-acting ). By matching heterotic one-loop gauge couplings, the authors express non-perturbative corrections as sums over Hecke operators and recover known one-loop Kahler corrections, highlighting a universal structure tied to target-space modular invariance (or its subgroup) across models. They provide explicit partition functions and unfolding techniques that map threshold integrals to modular-invariant sums, including automorphic forms in the freely-acting case. The results illuminate how corrections shape low-energy couplings and moduli stabilization prospects, and point toward broader universality and applications in other and orbifolds through duality and automorphic methods.

Abstract

We analyze N=2 (perturbative and non-perturbative) corrections to the effective theory in type I orbifold models where a dual heterotic description is available. These corrections may play an important role in phenomenological scenarios. More precisely, we consider two particular compactifications: the Bianchi-Sagnotti-Gimon-Polchinski orbifold and a freely-acting Z_2 x Z_2 orbifold with N=1 supersymmetry and gauge group SO(q) x SO(32-q). By exploiting perturbative calculations of the physical gauge couplings on the heterotic side, we obtain multi-instanton and one-loop string corrections to the Kähler potential and the gauge kinetic function for these models. The non-perturbative corrections appear as sums over relevant Hecke operators, whereas the one-loop correction to the Kähler potential matches the expression proposed in [1,2]. We argue that these corrections are universal in a given class of models where target-space modular invariance (or a subgroup of it) holds.

Paper Structure

This paper contains 20 sections, 85 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Bianchi-Sagnotti-Gimon-Polchinski orbifold
  3. Heterotic S-dual partition function
  4. Perturbative and non-perturbative corrections
  5. $E1$ instantons
  6. The $SO(q)\times SO(32-q)$ freely-acting orbifold
  7. Heterotic S-dual partition function
  8. Perturbative and non-perturbative corrections
  9. Universality of $\mathcal{N}=2$ corrections
  10. Concluding remarks
  11. Details on the computations
  12. The BSGP model
  13. Elliptic genera
  14. Zero orbit
  15. Degenerate orbits
  16. ...and 5 more sections

Figures (3)

  • Figure 1: E1 multi-instanton wrapping the first 2-torus, with induced worldvolume complex structure $\mathcal{U}$ given in (\ref{['uinst']}).
  • Figure 2: Representation of ${\cal F}_{\Gamma_0(2)}$, the fundamental domain for $\Gamma_0(2).$
  • Figure 3: The three possible types of $E1_r$ multi-instantons, $[h,g]=\{[1,0], [0,1], [1,1]\}$, wrapping torsional cycles in the $r$-th 2-torus in the $SO(q)\times SO(32-q)$ model, with induced worldvolume complex structure $\mathcal{U}_r^{[h,g]}$ given in eq.(\ref{['udisc']}). The continues lines represent the lattice of the underlying 2-torus. The orbifold generator reversing the transverse coordinates to the instanton, shifts the lattice to the dashed one.