RECORD
S-duality in Twistor Space
High Energy Physics - Theory · Submitted 6 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. | background 1.00 | 0.06 | 0.06 | asserted 1.00 |
| s1 | We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. | contribution 1.00 | 0.96 | 0.43 | asserted 1.00 |
| s2 | This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. | interpretation 0.47 | 0.40 | 0.16 | hedged possibility 0.89 |
| s3 | These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained. | interpretation 0.51 | 0.90 | 0.23 | asserted 0.93 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.
Human review
References
How the literature uses it
20 arXiv papers cite this in 58 sentences
Papers citing it · 44 sentences without a confident label
Builds on it 3 papers
-
In fact, this paper is an extension of the previous work [ref] where the same problem was addressed under the additional assumption that the allowed deformations preserve two continuous isometries.
Modularity, Quaternion-Kahler spaces and Mirror Symmetry · Introduction · 1.00
-
In Appendix [ref] we extend the procedure of [ref] and compute these corrections to the mirror map in our approximation.
D3-instantons, Mock Theta Series and Twistors · Instanton corrections in the large volume limit · 0.96
-
In Appendix [ref], generalizing the results of [ref] , we show how they can be included consistently with S-duality.
Multiple D3-instantons and mock modular forms II · S-duality · 0.96
Uses its method or tool 2 papers
-
For this purpose, it will be useful to borrow some methods from the work [ref] where a manifestly S-duality invariant twistorial construction of a QK manifold with two commuting isometries was provided.
D3-instantons, Mock Theta Series and Twistors · S-duality and mirror map · 0.93
-
As explained in [ref] , the S-duality transformations of such expressions can be greatly simplified by modifying the integration kernel by a $t$-independent term, at the cost of correcting the mirror map [ref].
Quantum hypermultiplet moduli spaces in N=2 string vacua: a review · Darboux coordinates and Eichler integrals · 0.83
Compares with it 2 papers
-
This mimicks the situation in the D1-D(-1) sector [ref] .
D3-instantons, Mock Theta Series and Twistors · Anomaly cancelation from mock theta series · 0.95
-
In this respect, we are in a much more complicated situation than in the case with two continuous isometries analyzed in [ref] .
Modularity, Quaternion-Kahler spaces and Mirror Symmetry · $SL(2,)$ action on the fiber, critical points and invariant kernel · 0.81
Cites it as background 6 papers
-
This question has been already addressed in the previous works [ref] .
Fivebrane instantons in Calabi-Yau compactifications · S-duality in twistor space · 0.86
-
Although much progress has been achieved recently in describing these instanton corrections [ref] (see [ref] for a review), a complete understanding is still lacking.
Heterotic-type II duality in twistor space · Introduction · 0.81
-
At classical level it has been found in [ref] and quantum corrections, including various instanton effects, have been included in [ref] .
Hypermultiplet metric and D-instantons · Type IIB and mirror symmetry · 0.92
What it cites · 83 sentences without a confident label
Builds on 2 papers
-
Having recast the construction of [ref] in a manifestly S-duality invariant fashion, the extension to S-duality invariant QK metrics with only two commuting isometries is then relatively straightforward, despite the fact that such metrics are no longer amenable to the Legendre transform construction.
Quantum mirror symmetry and twistors · Introduction · 1.00
-
This invariance has been shown in the D1-D(-1) sector [ref] , extending the results of the earlier work [ref] , and our goal is to extend this construction to D3-D1-D(-1)-instantons.
Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry · Twistorial description of $_H$ · 0.83
Uses the method or tool of 2 papers
-
Using [ref], we find that the Darboux coordinates in the patch $_0$ are given by [ref]
Linear perturbations of quaternionic metrics · Twistorial description of $_H$ · 0.93
-
Using [ref], we find that the Darboux coordinates in the patch $_0$ are given by [ref]
Twistors and Black Holes · Twistorial description of $_H$ · 0.93
Compares with 2 papers
-
Indeed, evaluating the integrals by residues, one can verify that [ref] coincides with the contact potential found in [ref] , while the quantum corrections [ref] reproduce the results in Eq. (5.2) [ref] up to δ_0^inst =∑_q_a ≥0 n_q_a^(0)∑_m,n' mδ_m,n, δσ^inst =-∑_q_a ≥0 n_q_a^(0)∑_m,n' (mτ_1+2n)δ_m,n,
Quantum mirror symmetry and twistors · The quantum mirror map revisited · 0.98
-
Indeed, evaluating the integrals by residues, one can verify that [ref] coincides with the contact potential found in [ref] , while the quantum corrections [ref] reproduce the results in Eq. (5.2) [ref] up to δ_0^inst =∑_q_a ≥0 n_q_a^(0)∑_m,n' mδ_m,n, δσ^inst =-∑_q_a ≥0 n_q_a^(0)∑_m,n' (mτ_1+2n)δ_m,n,
Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry · The quantum mirror map revisited · 0.98
Cites as support 2 papers
-
However, this symmetry descends from the usual S-duality action in ten-dimensional string theory, and there is overwhelming evidence that the modular subgroup $SL(2,)$ remains a symmetry at the quantum level (see [ref] and citations thereof).
Effects of D-instantons · Quantum corrections · 0.97
-
However, this symmetry descends from the usual S-duality action in ten-dimensional string theory, and there is overwhelming evidence that the modular subgroup $SL(2,)$ remains a symmetry at the quantum level (see [ref] and citations thereof).
Compactification of Type IIB String Theory on Calabi-Yau Threefolds · Quantum corrections · 0.97
Cites as background 12 papers
-
This has been understood in [ref] , based on the previous results of [ref] .
Hypermultiplets and Topological Strings · Twistorial description of $_H$ · 0.91
-
This has been understood in [ref] , based on the previous results of [ref] .
Twistors and Black Holes · Twistorial description of $_H$ · 0.91
-
This has been understood in [ref] , based on the previous results of [ref] .
Linear perturbations of quaternionic metrics · Twistorial description of $_H$ · 0.91
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.