Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

Bossard, Guillaume; Cosnier-Horeau, Charles; Pioline, Boris

doi:10.21468/SciPostPhys.7.3.028

SciPost Physics

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline

SciPost Phys. 7, 028 (2019) · published 5 September 2019

doi: 10.21468/SciPostPhys.7.3.028
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Abstract

Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nabla\phi)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order $e^{-1/g_3^2}$. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, as well as new predictions for higher genus perturbative contributions. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact $\nabla^2 F^4$ effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order $e^{-R}$ from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order $e^{-R^2}$ from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.3.028
TI  - Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
PY  - 2019/09/05
UR  - https://scipost.org/SciPostPhys.7.3.028
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 3
SP  - 028
A1  - Bossard, Guillaume
AU  - Cosnier-Horeau, Charles
AU  - Pioline, Boris
AB  - Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nabla\phi)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order $e^{-1/g_3^2}$. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, as well as new predictions for higher genus perturbative contributions. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact $\nabla^2 F^4$ effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order $e^{-R}$ from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order $e^{-R^2}$ from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.
ER  -

@Article{10.21468/SciPostPhys.7.3.028,
	title={{Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds}},
	author={Guillaume Bossard and Charles Cosnier-Horeau and Boris Pioline},
	journal={SciPost Phys.},
	volume={7},
	pages={028},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.3.028},
	url={https://scipost.org/10.21468/SciPostPhys.7.3.028},
}

Cited by 9

Ontology / Topics

See full Ontology or Topics database.

BPS dyons Black holes CHL orbifolds

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Guillaume Bossard,
¹ ² Charles Cosnier-Horeau,
² Boris Pioline

Funder for the research work leading to this publication

Agence Nationale de la Recherche [ANR]