Instanton corrections to the universal hypermultiplet and automorphic forms on {$SU(2,1)$}

• DOI: 10.4310/cntp.2010.v4.n1.a5
• Publication Date: 2013-08-30T22:59:03Z
• Authors: Ling Bao; Axel Kleinschmidt; Bengt E.W. Nilsson; Daniel Persson; Boris Pioline
• Keywords: Instanton; Compactification (mathematics)

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 symmetric SU (2, 1)/(SU (2) × U (1)).To determine quantum corrections this metric, we posit that discrete subgroup of continuous isometry group 1), namely Picard modular 1; Z[i]), must remain unbroken exact metric -including all perturbative and non-perturbative corrections.This assumption expected be valid when admits complex multiplication Z[i].Based hypothesis, construct an Z[i])-invariant, non-holomorphic Eisenstein series, tentatively propose series provides contact potential twistor over universal space.We analyze its non-Abelian Fourier expansion, show Abelian coefficients take required form for instanton due Euclidean D2-branes wrapping special Lagrangian submanifolds, NS5-branes entire threefold, respectively.While tentative proposal fails reproduce correct one-loop correction, consistency expansion with physics expectations strong support usefulness constraining space.C.1.Analysis norm constraint 253 C.1.1 Multiplicative structure.253 C.1.2Restriction fundamental domain.254 C.2. Rewriting measure 257 C.2.1 Evaluation q (d) ν s (q).257 C.2.2 measure.259