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Instanton Correctio...
Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1).
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- Nilsson, Bengt E W, 1952 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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- Bao, Ling, 1980 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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- Persson, Daniel, 1978 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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Kleinschmidt, Axel (author)
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Pioline, Boris (author)
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(creator_code:org_t)
- 2010
- 2010
- English.
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In: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 4:1, s. 187-266
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Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Fysik -- Subatomär fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Subatomic Physics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publication and Content Type
- art (subject category)
- ref (subject category)
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