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Report number	arXiv:1702.01926 ; CERN-TH-2017-028 ; CPHT-RR004.022017
Title	Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
Related title	Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
Author(s)	Bossard, Guillaume (Ecole Polytechnique, CPHT) ; Cosnier-Horeau, Charles (Ecole Polytechnique, CPHT ; Paris, LPTHE) ; Pioline, Boris (Paris, LPTHE ; CERN)
Publication	2017-07-31
Imprint	2017-02-07
Number of pages	72
Note	42+19 pages; v3: references added, few misprints corrected, several clarifications in section 2.1 and 2.2
In:	SciPost Phys. 3 (2017) 008
DOI	10.21468/SciPostPhys.3.1.008
Subject category	hep-th ; Particle Physics - Theory
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.
Copyright/License	arXiv nonexclusive-distrib. 1.0 Preprint: © 2016-2025 CERN (License: CC-BY-4.0)

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