Harmonic Analysis on Symmetric Spaces and Applications I

Terras, Audrey

doi:10.1007/978-1-4612-5128-6

Cited by 342 publications

(416 citation statements)

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“…As regards the power solutions (5.12a) and (5.12b), summing them over the SL(2, Z) gives rise to the non-holomorphic modular (automorphic) forms called the Eisenstein series [45], 13) with s = −1/2 and s = 3/2, respectively. To be well defined, the sum in eq.…”

Section: D-instantons In N=2 Supergravitymentioning

confidence: 99%

Summing up D-instantons in N=2 supergravity

Ketov

2003

Nuclear Physics B

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The non-perturbative quantum geometry of the Universal Hypermultiplet (UH) is investigated in N=2 supergravity. The UH low-energy effective action is given by the four-dimensional quaternionic non-linear sigma-model having an U(1) × U(1) isometry. The UH metric is governed by the single real pre-potential that is an eigenfunction of the Laplacian in the hyperbolic plane. We calculate the classical prepotential corresponding to the standard (Ferrara-Sabharwal) metric of the UH arising in the Calabi-Yau compactification of type-II superstrings. The non-perturbative quaternionic metric, describing the D-instanton contributions to the UH geometry, is found by requiring the SL(2, Z) modular invariance of the UH pre-potential. The prepotential found is unique, while it coincides with the D-instanton function of Green and Gutperle, given by the order-3/2 Eisenstein series. As a by-product, we prove cluster decomposition of D-instantons in curved spacetime. The non-perturbative UH pre-potential interpolates between the perturbative (large CY volume) region and the superconformal (Landau-Ginzburg) region in the UH moduli space. We also calculate a non-perturbative scalar potential in the hyper-Kähler limit, when an abelian isometry of the UH metric is gauged in the presence of D-instantons.

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Section: D-instantons In N=2 Supergravitymentioning

confidence: 99%

Summing up D-instantons in N=2 supergravity

Ketov

2003

Nuclear Physics B

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“…Gutzwiller [5]). Discussions of the fundamental domain for SL(2, Z) and some of its applications can be found in Terras [17,, Similar applications are envisioned for T3 = SL(3,Z). We have left out the normalizing factors which are usually introduced here.…”

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confidence: 89%

“…One would have to take logj to obtain noneuclidean coordinates. For the details of the results mentioned above, as well as background for the rest of this paper, see Terras [17]. Our goal here is to come to an understanding of the fundamental domain for SL (3, Z) which is as good as that for SL(2, Z).…”

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confidence: 99%

Hecke operators and the fundamental domain for 𝑆𝐿(3,𝑍)

Gordon¹,

Grenier²,

Terras³

1987

Math. Comp.

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“…Note that since 3 2 6 4 π π = , the same quantity as in the 2D-case (16) appears on the right hand side of (49). The orthonormal spherical harmonic functions in (49) are often defined with Legendre polynomials and complex valued functions [47]. For our purposes, however, it is important to normalize the zero order and second order harmonics into one single set.…”

Section: Diagonalizing the Hessian Mapping Derivatives To Harmonicsmentioning

confidence: 99%

“…In fact, for the 2D-case, the so-called complex moments, correspond to the orthogonal (but not normalized) basis set of circular harmonics given in complex form. Likewise, in the 3D-case, the complex moments correspond to orthogonal spherical harmonic functions in complex form as given in [47]. However, the two domains in (12) and (50) are not quite symmetric.…”

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confidence: 99%