Gravitational dressing of D-instantons

Abstract

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.

Universal hypermultiplet metrics

“…Since the quaternionic and hyper-Kähler conditions are not compatible, the canonical form (4.1) should be revised. 7 Nevertheless, the exact quaternionic metric is governed by the same three-dimensional Toda equation (4.7) [15]. Indeed, when using another (Tod) Ansatz [41]…”

“…Based on the fact that both hyper-Kähler and quaternionic metrics under consideration are governed by the same Toda equation, a natural mechanism 8 of generating the quaternionic metrics from known hyper-Kähler metrics in the same (four) dimensions arises: first, one deduces a solution to the Toda equation (4.7) from a given fourdimensional hyper-Kähler metric having a non-triholomorphic or rotational isometry, by rewriting it to the form (4.1), and then one inserts the obtained exact solution into the quaternionic Ansatz (5.2) to deduce the corresponding quaternionic metric with the same isometry. Being applied to the D-instantons, this mechanism results in their dressing with respect to 4d, N=2 supergravity background [15].…”

“…The 'cosmological' constant Λ can be considered as the most relevant parameter of the deformation that converts a given UH hyper-Kähler metric into the 'gravitationally dressed' quaternionic UH metric via eq. ( 5.2), based on the same solution to the Toda equation (4.7) [15].…”

Directional Dark Matter Search with Super-Resolution Nuclear Emulsion

“…Nuclear emulsion is the most accurate 3-dimensional position detector with submicron scale resolution. It has played a key role in the discovery of new particles and phenomena all along the particle physics history, e.g., [12,13,14]. For the dark matter search, nuclear recoil tracks in a solid-state detector are expected to be shorter than a micron, given their low speed, around O(100) km/s.…”