| 1. |
- Fleig, Philipp, et al.
(författare)
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Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
- 2014
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 8:1, s. 41-100
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on E_9(R), E_10(R) and E_11(R) corresponding to certain degenerate principal series at the values s=3/2 and s=5/2 that were studied in 1204.3043. We show that these Eisenstein series have very simple Fourier coefficients as expected for their role as supersymmetric contributions to the higher derivative couplings R^4 and \partial^{4} R^4 coming from 1/2-BPS and 1/4-BPS instantons, respectively. This suggests that there exist minimal and next-to-minimal unipotent automorphic representations of the associated Kac-Moody groups to which these special Eisenstein series are attached. We also provide complete explicit expressions for degenerate Whittaker vectors of minimal Eisenstein series on E_6(R), E_7(R) and E_8(R) that have not appeared in the literature before.
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| 2. |
- Gaberdiel, Matthias R., et al.
(författare)
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Generalized Mathieu Moonshine
- 2013
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 7:1, s. 145-223
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Tidskriftsartikel (refereegranskat)abstract
- The Mathieu twisted twining genera, i.e., the analogues of Norton's generalized Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour under modular transformations is controlled by a 3-cocycle in H-3(M-24, U(1)), just as for the case of holomorphic orbifolds. This suggests that a holomorphic VOA may be underlying Mathieu Moonshine.
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| 3. |
- Nilsson, Bengt E W, 1952, et al.
(författare)
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Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2,1).
- 2010
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 4:1, s. 187-266
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Persson, Daniel, 1978, et al.
(författare)
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Second-quantized Mathieu moonshine
- 2014
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 8:3, s. 403-509
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Tidskriftsartikel (refereegranskat)abstract
- We study the second-quantized version of the twisted twining genera of generalized Mathieu moonshine, and prove that they give rise to Siegel modular forms with infinite product representations. Most of these forms are expected to have an interpretation as twisted partition functions counting 1/4 BPS dyons in type II superstring theory on K3 x T-2 or in heterotic CHL-models. We show that all these Siegel modular forms, independently of their possible physical interpretation, satisfy an "S-duality" transformation and a "wall-crossing formula". The latter reproduces all the eta-products of an older version of generalized Mathieu moonshine proposed by Mason in the 1990s. Surprisingly, some of the Siegel modular forms we find coincide with the multiplicative (Borcherds) lifts of Jacobi forms in umbral moonshine.
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