Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1)

Persson, Daniel,1978Chalmers tekniska högskola,Chalmers University of Technology (author)

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) x 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 unbroken in the exact metric -- including all perturbative and non perturbative quantum corrections. 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 reproduce the correct one-loop correction, the consistency of the Fourier expansion with physics expectations provides strong support for the utility of the Picard modular group in constraining the quantum moduli space.

Nilsson, Bengt E W,1952Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)tfebn (author)
Bao, Ling,1980Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)f99ling (author)
Kleinschmidt, Axel (author)
Pioline, Boris (author)
Chalmers tekniska högskola (creator_code:org_t)

By the author/editor: Persson, Daniel, ...; Nilsson, Bengt E ...; Bao, Ling, 1980; Kleinschmidt, Ax ...; Pioline, Boris

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Subatomic Physic ...

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