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R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

A. Gregori, E. Kiritsis, C. Kounnas, N. A. Obers, P. M. Petropoulos, B. Pioline

TL;DR

This work analyzes four-derivative gravitational couplings in string vacua with N=4 supersymmetry, focusing on R^2-type terms and their non-perturbative dualities between heterotic and type II theories as well as type II U-duality. The authors show that CP-even R^2 terms in certain N=4 models are captured by one-loop thresholds, while dualities map these to NS5-brane instanton sums on dual sides; CP-odd couplings relate to axionic interactions with similar instanton structures, though some apparent holomorphic anomalies are resolved via Chern-Simons formulations. They compute helicity supertraces to organize BPS contributions and derive moduli-dependent thresholds for six- and four-dimensional vacua, including reduced-rank models where S- or T-duality is broken to subgroups like Γ(2). The results provide concrete non-perturbative tests of heterotic/type II duality and illustrate how instanton corrections encode strong-coupling physics, occasionally restoring higher supersymmetry in certain limits. Overall, the paper advances understanding of how higher-derivative couplings encode duality and non-perturbative dynamics in N=4 string ground states, with implications for constructing controlled non-perturbative vacua.

Abstract

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six- and four-dimensional type II string ground states with N=4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4,0) and (2,2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R^2 coupling on the (2,2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4,0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction a.R\wedge R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2,Z)_S S-duality symmetry to a Γ(2)_S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N=4 models in which N=8 supersymmetry appears at strong coupling.

R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

TL;DR

This work analyzes four-derivative gravitational couplings in string vacua with N=4 supersymmetry, focusing on R^2-type terms and their non-perturbative dualities between heterotic and type II theories as well as type II U-duality. The authors show that CP-even R^2 terms in certain N=4 models are captured by one-loop thresholds, while dualities map these to NS5-brane instanton sums on dual sides; CP-odd couplings relate to axionic interactions with similar instanton structures, though some apparent holomorphic anomalies are resolved via Chern-Simons formulations. They compute helicity supertraces to organize BPS contributions and derive moduli-dependent thresholds for six- and four-dimensional vacua, including reduced-rank models where S- or T-duality is broken to subgroups like Γ(2). The results provide concrete non-perturbative tests of heterotic/type II duality and illustrate how instanton corrections encode strong-coupling physics, occasionally restoring higher supersymmetry in certain limits. Overall, the paper advances understanding of how higher-derivative couplings encode duality and non-perturbative dynamics in N=4 string ground states, with implications for constructing controlled non-perturbative vacua.

Abstract

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six- and four-dimensional type II string ground states with N=4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4,0) and (2,2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R^2 coupling on the (2,2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4,0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction a.R\wedge R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2,Z)_S S-duality symmetry to a Γ(2)_S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N=4 models in which N=8 supersymmetry appears at strong coupling.

Paper Structure

This paper contains 21 sections, 220 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Perturbative and instanton corrections to $R^2$ couplings
  3. One-loop corrections in six-dimensional type IIA and IIB theories
  4. Type II superstring on $K3$: a reminder
  5. One-loop three-graviton scattering amplitude in six dimensions
  6. One-loop gravitational corrections in four-dimensional type II models
  7. Four-dimensional $N=4$ supersymmetry and its BPS states
  8. Gravitational thresholds in four dimensions
  9. Two-graviton--$N$-moduli scattering amplitude
  10. Gravitational thresholds and helicity supertraces
  11. Gravitational thresholds in ordinary type II on $K3 \times T^2$
  12. Helicity supertraces and $R^2$ corrections
  13. Decompactification limit of CP-even couplings: a puzzle
  14. CP-odd couplings and holomorphic anomalies
  15. From type II to heterotic string
  16. ...and 6 more sections

Figures (1)

  • Figure 1: The cube of duality, decompactification and strong/weak coupling relations