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Heterotic-type II duality in twistor space
High Energy Physics - Theory · Submitted 10 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the `double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string.
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The abstract, sentence by sentence
Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the `double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the double scaling limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4,n,Z) obtained by Borcherds' lift.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. | background 1.00 | 0.04 | 0.07 | hedged possibility 0.85 |
| s1 | In particular, it must share the same hypermultiplet moduli space. | background 0.98 | 0.05 | 0.05 | asserted 0.82 |
| s2 | Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the `double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. | contribution 0.99 | 0.94 | 0.61 | asserted 1.00 |
| s3 | We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the double scaling limit. | contribution 0.74 | 0.89 | 0.06 | asserted 0.70 |
| s4 | As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4,n,Z) obtained by Borcherds' lift. | result 0.79 | 0.91 | 0.09 | asserted 1.00 |
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The paper
Original abstract
Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the `double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the double scaling limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4,n,Z) obtained by Borcherds' lift.
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References
How the literature uses it
6 arXiv papers cite this in 13 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 4 papers
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We first recall the basic features of heterotic/type II duality in the hypermultiplet sector [ref] .[Since the hypermultiplet moduli space is independent of the $T^2$ moduli, one may as well work in 6 dimensions, and use heterotic/F-theory duality, where F-theory is compactified on the same CY threefold $$.] According to this duality, $E_8×E_8$ heterotic string theory compactified on $×T^2$ is equivalent to type IIA string theory compactified on a Calabi-Yau threefold $$, or to type IIB string theory compactified on the mirror CY threefold $$.
N=2 Heterotic-Type II duality and bundle moduli · Heterotic/type II duality in hypermultiplet sector · 1.00
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For other aspects of hypermultiplet moduli map, see e.g. [ref] and references therein.
Heterotic-Type IIA Duality and Degenerations of K3 Surfaces · Lg degeneration of Lg-elliptic K3 surfaces · 0.95
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For some references on heterotic hypermultiplet moduli spaces, see e.g. [ref] .
The geometry of hypermultiplets · QK's from String Theory · 0.98
What it cites · 60 sentences without a confident label
Uses the method or tool of 3 papers
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One introduces Darboux coordinates [ref]
Twistors and Black Holes · Type II Darboux coordinates · 0.88
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One introduces Darboux coordinates [ref]
Linear perturbations of quaternionic metrics · Type II Darboux coordinates · 0.88
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The solution to [ref] follows by a simple Penrose-type contour integral Ψ= ∑_j∮_C_j ν ij_(-1) ∼r ∑_j∮_C_j t/t νij_(-1) , where $$ is the contact one-form [ref], $r=e^Φ= e^-(ρ+R)/2$ is the contact potential, $ν$ is the projective coordinate which can be absorbed due to the homogeneity of $ij_(-1)$, and $C_j$ is a contour on $S^2$ surrounding the patch $_j$.[As in [ref] , the sum over patches does not depend on the free index $i$ due to the standard consistency conditions on the holomorphic functions $ij_(-1)$.] Our goal is to identify a holomorphic function $H_(-1)$ and the associated contour $C$ which, after Penrose transform, produces a function $Ψ$ on $$ which behaves as $e^-2πS_inst$ in the large volume limit.
Linear perturbations of Hyperkahler metrics · A twistorial origin for scalar-valued worldsheet instantons · 0.84
Compares with 1 paper
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Comparing the metrics [ref] and [ref] on the HM moduli space, we find that the two agree provided [ref] [To translate to the notations in [ref] , set [equation] ] r= e^-1/2(ρ+R) , s=^-(ρ-R) -B_2 , c^A= v^A, _A=B_A-B_2 v_A, σ=- 2B_1 - v^A B_A .
Heterotic-Type II duality in the hypermultiplet sector · Classical limit and duality map · 0.98
Cites as background 28 papers
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The duality map between heterotic and type II variables in this limit, first discussed in [ref] and completed recently in [ref] , is recalled in [ref] below.
Aspects of the Hypermultiplet Moduli Space in String Duality · Introduction · 0.92
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The duality map between heterotic and type II variables in this limit, first discussed in [ref] and completed recently in [ref] , is recalled in [ref] below.
Heterotic-Type II duality in the hypermultiplet sector · Introduction · 0.92
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Although much progress has been achieved recently in describing these instanton corrections [ref] (see [ref] for a review), a complete understanding is still lacking.
Conifold singularities, resumming instantons and non-perturbative mirror symmetry · Introduction · 0.81
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