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BPS states and BPS amplitudes in string theory

Abstract : Motivated by precision counting of BPS black hole microstates in four dimensions, we analyse four- and six- derivative coupling in the low energy effective action of a three-dimensional string vacua with 16 supercharges. Based on perturbative calculation up to two loops, supersymmetry and duality arguments, we conjecture that the exact coefficient of the four- and six- derivative effective interaction in the gauge fields are given by genus one and two modular integrals of non-perturbative partition functions, and meromorphic modular forms known from previous work. We then show that these proposals reproduce known perturbative corrections at weak heterotic coupling limit, and that some of their non-perturbative instantonic corrections reproduce the counting of half and quarter-BPS black hole states, respectively, in the limit of decompactification from three to four dimensions. Regarding the quarter-BPS black hole counting, we recover for the simplest primitive vectors the BPS index predicted by the Dijkgraaf-Verlinde-Verlinde formula, including the detailed moduli dependence, and we then give predictions for all other types of primitive vectors. We also extract two-instanton corrections from pairs of half-BPS black hole states, demonstrating consistency with supersymmetry constraints.
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  • HAL Id : tel-02890267, version 1

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Charles Cosnier-Horeau. BPS states and BPS amplitudes in string theory. High Energy Physics - Theory [hep-th]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS424⟩. ⟨tel-02890267⟩

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