Abstract
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 pre-potential 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 pre-potential 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.
| Original language | English |
|---|---|
| Pages (from-to) | 365-388 |
| Number of pages | 24 |
| Journal | Nuclear Physics B |
| Volume | 649 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 20 Jan 2003 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
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Summing up D-instantons in N = 2 supergravity. / Ketov, Sergei V.
In: Nuclear Physics B, Vol. 649, No. 1-2, 20.01.2003, p. 365-388.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Summing up D-instantons in N = 2 supergravity
AU - Ketov, Sergei V.
PY - 2003/1/20
Y1 - 2003/1/20
N2 - 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 pre-potential 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 pre-potential 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.
AB - 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 pre-potential 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 pre-potential 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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U2 - 10.1016/S0550-3213(02)01026-X
DO - 10.1016/S0550-3213(02)01026-X
M3 - Review article
VL - 649
SP - 365
EP - 388
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 1-2
ER -