Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1).
Artikel i vetenskaplig tidskrift, 2010

Abstract: The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X , corresponding to the “universal hypermultiplet”, is described at tree-level by the symmetric space SU(2,1)/(SU(2)×U(1)). To determine the quantum corrections to this metric, we posit that a discrete subgroup of the continuous tree-level isometry group SU(2,1), namely the Picard modular group SU(2,1;Z[i]), must remain un- broken in the exact metric – including all perturbative and non-perturbative quantum cor- rections. This assumption is expected to be valid when X admits complex multiplication by Z[i]. Based on this hypothesis, we construct an SU(2,1;Z[i])-invariant, non-holomorphic Eisenstein series, and tentatively propose that this Eisenstein series provides the exact contact potential on the twistor space over the universal hypermultiplet moduli space. We analyze its non-Abelian Fourier expansion, and show that the Abelian and non-Abelian Fourier coefficients take the required form for instanton corrections due to Euclidean D2- branes wrapping special Lagrangian submanifolds, and to Euclidean NS5-branes wrapping the entire Calabi-Yau threefold, respectively. While this tentative proposal fails to repro- duce the correct one-loop correction, the consistency of the Fourier expansion with physics expectations provides strong support for the usefulness of the Picard modular group in constraining the quantum moduli space.


Bengt E W Nilsson

Chalmers, Teknisk fysik, Matematisk fysik

Ling Bao

Chalmers, Teknisk fysik, Matematisk fysik

Daniel Persson

Chalmers, Teknisk fysik, Matematisk fysik

Axel Kleinschmidt

Boris Pioline

Communications in Number Theory and Physics

1931-4523 (ISSN) 1931-4531 (eISSN)

Vol. 4 187-266


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