Automorphic instanton partition functions on Calabi-Yau threefolds

• We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X × S 1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that when the theory in three dimensions exhibits an arithmetic "U-duality" symmetry G(ℤ) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. In the case of four-dimensional N = 2 theories on ℝ × S 1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function is a holomorphic section on the twistor space Z over M.

Subject headings

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

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