Quantum Non-linear Sigma-Models

Ketov, Sergei V.

doi:10.1007/978-3-662-04192-5

Cited by 127 publications

(148 citation statements)

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“…To calculate these deformations, it is natural to put the metric (2) into the canonical form (in terms of two potentials W and u, and a one-form Θ 1 ) [13,15],…”

Section: Quantum Hyper-kähler Uh Metricmentioning

confidence: 99%

“…which is known as the SU(∞) Toda field equation [19,15] since it appears in the large-N limit of the standard two-dimensional Toda system for SU(N).…”

Section: Quantum Hyper-kähler Uh Metricmentioning

confidence: 99%

“…This is known as the Toda frame for a hyper-Kähler metric [14,15]. It is not difficult to verify that the separable solution (25) is generated from the Eguchi-Hanson (hyper-Kähler) metric along these lines [15].…”

Section: Exact Quaternionic Solutionsmentioning

confidence: 99%

“…It is not difficult to verify that the separable solution (25) is generated from the Eguchi-Hanson (hyper-Kähler) metric along these lines [15]. A highly non-trivial solution to the Toda equation (10) follows from the Atiyah-Hitchin (hyper-Kähler) metric [17].…”

Section: Exact Quaternionic Solutionsmentioning

confidence: 99%

“…in terms of the standard complete elliptic integrals of the first and second kind, K(k) and E(k), respectively [15]. The associated solution to the Toda equation (10) reads [24,15] e u = 1 16 K 2 (k) sin 2 ϑ 1 + k 2 sinh 2 ν .…”

Section: Exact Quaternionic Solutionsmentioning

confidence: 99%

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Gravitational dressing of D-instantons

Ketov¹

2001

Physics Letters B

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The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi-Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi-Yau 3-cycles, and they are known as the D-instantons. The exact universal hypermultiplet metric is governed by a quaternionic potential that satisfies the SU(∞) Toda equation. The mechanism is proposed, which elevates any four-dimensional hyper-Kähler metric with a rotational isometry to the quaternionic metric of the same dimension. A generic separable solution to the Toda equation appears to be related to the EguchiHanson metric, whereas another solution originating from the Atiyah-Hitchin metric describes the gravitationally dressed (mixed) D-instantons.

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“…To calculate these deformations, it is natural to put the metric (2) into the canonical form (in terms of two potentials W and u, and a one-form Θ 1 ) [13,15],…”

Section: Quantum Hyper-kähler Uh Metricmentioning

confidence: 99%

“…which is known as the SU(∞) Toda field equation [19,15] since it appears in the large-N limit of the standard two-dimensional Toda system for SU(N).…”

Section: Quantum Hyper-kähler Uh Metricmentioning

confidence: 99%