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

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.

arXiv comment6 pages

References in corpus (19)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Four-dimensional wall-crossing via three-dimensional field theory
• Effects of D-instantons
• Counting Dyons in N=4 String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Exact Counting of Black Hole Microstates
• Four Dimensional String/String/String Triality
• Maximally Supersymmetric String Theories in D<10
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Strong-Weak Coupling Duality in Three Dimensional String Theory
• Two-loop superstrings and S-duality
• Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory
• BPS black holes, quantum attractor flows and automorphic forms
• Calculable e^{-1/λ} Effects
• Rankin-Selberg methods for closed string amplitudes

Cited by in corpus (11)

• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Cancellation of divergences up to three loops in exceptional field theory
• Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Heterotic sigma models on $T^8$ and the Borcherds automorphic form ${\Phi }_{12}$
• Mock modularity from black hole scattering states
• Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
• Some comments on symmetric orbifolds of K3
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model