## Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline

SciPost Phys. 3, 008 (2017) · published 31 July 2017

- doi: 10.21468/SciPostPhys.3.1.008
- Submissions/Reports

### Abstract

Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form $F(\Phi) (\nabla\Phi)^4$ in a class of string vacua known as CHL $\mathbb{Z}_N$ heterotic orbifolds with $N$ prime, generalizing our previous work which dealt with the case of heterotic string on $T^6$. We derive the Ward identities that $F(\Phi)$ must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of $F(\Phi)$, and show that it reproduces the correct tree-level and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact $F^4$ coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in $D=4$ and $D=3$, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.

### Cited by 9

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Guillaume Bossard, -
^{1}^{2}^{3}^{4}Charles Cosnier-Horeau, -
^{2}^{3}^{4}^{5}Boris Pioline

^{1}Université Paris-Saclay / University of Paris-Saclay^{2}Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]^{3}Laboratoire de Physique Théorique et Hautes Energies / Laboratory of Theoretical and High Energy Physics [LPTHE]^{4}Sorbonne Université / Sorbonne University^{5}Organisation européenne pour la recherche nucléaire / European Organization for Nuclear Research [CERN]