Membrane instantons from mirror symmetry

Robles-Llana, Daniel; Saueressig, Frank; Theis, Ulrich

doi:10.4310/cntp.2007.v1.n4.a3

Cited by 40 publications

(81 citation statements)

References 39 publications

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“…The progress mentioned above was related with the developments of twistorial methods which provide an efficient parametrization of QK geometries [7][8][9]. Combining these methods with the symmetries expected to survive at quantum level, a large class of instanton corrections to the HM moduli space has been found [10][11][12][13][14][15][16][17] (see [18,19] for reviews). Although the description of few types of instantons remains still unknown, the complete non-perturbative picture for this class of compactifications seems to be already not far from our reach.…”

Section: Jhep02(2015)176mentioning

confidence: 99%

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Hypermultiplet metric and D-instantons

Alexandrov

Banerjee

2015

J. High Energ. Phys.

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Abstract:We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kähler metric which is a non-trivial deformation of the local c-map. In the four-dimensional case corresponding to the universal hypermultiplet, our metric fits the Tod ansatz and provides an exact solution of the continuous Toda equation. We also analyze the fate of the curvature singularity of the perturbative metric by deriving an S-duality invariant equation which determines the singularity hypersurface after inclusion of the D(-1)-instanton effects.

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Section: Jhep02(2015)176mentioning

confidence: 99%

“…(C.3) 11 To get all these results as well as the ones which follow below, it is crucial to take into account the condition of mutual locality, which takes the form qp ′ = q ′ p and implies, in particular, that ZγZ γ ′ =ZγZ γ ′ and vZγ =vZγ.…”

Section: Match With the Tod Ansatzmentioning

confidence: 99%

Hypermultiplet metric and D-instantons

Alexandrov

Banerjee

2015

J. High Energ. Phys.

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“…Using these techniques, combining earlier results on the twistorial description of the perturbative metric and of D1-D(-1)-instantons [22][23][24][25] and taking inspiration from a similar construction in the context of gauge theories [26], a general construction of the Dinstanton corrected HM moduli space was laid out in [27,28], in terms of the generalized Donaldson-Thomas (DT) invariants Ω(γ; z) which count D-instantons. For reasons that will become clear below, we refer to the construction of [27,28] as the 'type IIA' construction.…”

Section: Introductionmentioning

confidence: 99%

D3-instantons, mock theta series and twistors

Alexandrov

Manschot

Pioline

2013

J. High Energ. Phys.

101

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The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

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“…More recently, the S-duality of type IIB string theory was used to derive instanton corrections to the hypermultiplet moduli space in general type II compactifications on a Calabi-Yau X , for a subset of instanton configurations which preserve the toric isometries [37,38]: namely D(−1), F1 and D1 instantons in type IIB, or D2-branes in an appropriate Lagrangian sublattice in H 3 (X, Z) (i.e. "wrapping A-cycles only", for a suitable choice of symplectic basis of A and B-cycles) in type IIA.…”

Section: Introductionmentioning

confidence: 99%

Linear Perturbations of Hyperkähler Metrics

et al. 2009

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Abstract. We study general linear perturbations of a class of 4d real-dimensional hyperkäh-ler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic functions of 2d + 1 variables, as opposed to the functions of d + 1 variables controlling the unperturbed metric. Such deformations generically break all tri-holomorphic isometries of the unperturbed metric. Geometrically, these functions generate the symplectomorphisms which relate local complex Darboux coordinate systems in different patches of the twistor space. The deformed Kähler potential follows from these data by a Penrose-type transform. As an illustration of our general framework, we determine the leading exponential deviation of the Atiyah-Hitchin manifold away from its negative mass Taub-NUT limit. Mathematics Subject Classification (2000). 53C26, 53C28, 53C80.

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Membrane instantons from mirror symmetry

Cited by 40 publications

References 39 publications

Hypermultiplet metric and D-instantons

Hypermultiplet metric and D-instantons

D3-instantons, mock theta series and twistors

Linear Perturbations of Hyperkähler Metrics

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