# Protected couplings and BPS dyons in half-maximal supersymmetric string vacua

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Abstract : We analyze four- and six-derivative couplings in the low energy effective action of $D=3$ string vacua with half-maximal supersymmetry. In analogy with an earlier proposal for the $(\nabla\Phi)^4$ coupling, we propose that the $\nabla^2(\nabla\Phi)^4$ coupling is given exactly by a manifestly U-duality invariant genus-two modular integral. In the limit where a circle in the internal torus decompactifies, the $\nabla^2(\nabla\Phi)^4$ coupling reduces to the $D^2 F^4$ and $R^2 F^2$ couplings in $D=4$, along with an infinite series of corrections of order $e^{-R}$, from four-dimensional 1/4-BPS dyons whose wordline winds around the circle. Each of these contributions is weighted by a Fourier coefficient of a meromorphic Siegel modular form, explaining and extending standard results for the BPS index of 1/4-BPS dyons.
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Submitted on : Monday, December 19, 2016 - 9:39:19 AM
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### Citation

Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline. Protected couplings and BPS dyons in half-maximal supersymmetric string vacua. Modern Physics Letters B, World Scientific Publishing, 2016, 765, pp.377 - 381. ⟨10.1016/j.physletb.2016.12.035⟩. ⟨hal-01419203⟩

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