SciPost Physics

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

• doi: 10.21468/SciPostPhys.3.1.008
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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.

• Chattopadhyaya et al., Gravitational couplings in $$ \mathcal{N}=2 $$ string compactifications and Mathieu Moonshine
  J. High Energ. Phys. 2018, 211 (2018) [Crossref]
• Bossard et al., Cancellation of divergences up to three loops in exceptional field theory
  J. High Energ. Phys. 2018, 100 (2018) [Crossref]
• Nally, Exact half-BPS black hole entropies in CHL models from Rademacher series
  J. High Energ. Phys. 2019, 60 (2019) [Crossref]
• Fischbach et al., Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model
  J. High Energ. Phys. 2021, 157 (2021) [Crossref]
• Gerken et al., Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
  J. High Energ. Phys. 2019, 52 (2019) [Crossref]
• Eloy et al., U duality and α′ corrections in three dimensions
  Phys. Rev. D 108, 026015 (2023) [Crossref]
• Volpato, Some comments on symmetric orbifolds of K3
  J. High Energ. Phys. 2019, 82 (2019) [Crossref]
• Persson et al., Dualities in CHL-models
  J. Phys. A: Math. Theor. 51, 164002 (2018) [Crossref]
• Bossard et al., Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
  SciPost Phys. 7, 028 (2019) [Crossref]