Heterotic-Type IIA Duality and Degenerations of K3 Surfaces

Andreas P. Braun; Taizan Watari

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Heterotic-Type IIA Duality and Degenerations of K3 Surfaces

Andreas P. Braun, Taizan Watari

High Energy Physics - Theory · Submitted 21 Apr 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.36 · mentions code or data availability 0.01.

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We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic--type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories.	contribution 0.76	0.85	0.06	asserted 0.90
s1	Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification.	method 0.46	0.27	0.08	hedged possibility 0.60
s2	This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration.	limitation 0.49	0.35	0.09	asserted 1.00
s3	Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory.	contribution 0.78	0.88	0.23	asserted 1.00
s4	The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side.	method 0.64	0.34	0.17	asserted 0.96
s5	Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds.	interpretation 0.64	0.53	0.15	asserted 0.97
s6	Starting from well-known examples of heterotic--type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.	interpretation 0.78	0.37	0.22	hedged possibility 0.90

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Original abstract

We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic--type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Bounds on Species Scale and the Distance Conjecture
hep-th 2023-03 conditional novelty 6.0 of 10

The species scale, the energy at which gravity stops being described by Einstein's theory, cannot change faster than exponentially with distance in scalar field space.
Tensionless Strings and the Weak Gravity Conjecture
hep-th 2018-08 conditional novelty 6.0 of 10

A gauge coupling taken to zero at fixed Planck mass sits at infinite distance in moduli space, where a critical heterotic string becomes tensionless and its charged excitations populate a sublattice that satisfies the...

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15 arXiv papers cite this in 36 sentences

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Papers citing it · 26 sentences without a confident label

Builds on it 1 paper

Also, a part of the idea (using $Δh^2,1_R$) for invariants in the case $Λ_S = +2$ in [ref] has been incorporated as a part of $Φ^(R)$ for general $Λ_S$'s in this article, but a bit more idea beyond $Δh^2,1_R$ in [ref] has not been generalized to other $Λ_S$'s, or brought into the language of world-sheet CFT in this article.

Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua · Open Questions · 0.93

Cites it as support 1 paper

In this article, we only consider regular K3-fibrations, because that is when one can find Heterotic dual descriptions without (generalization of) NS5-branes [ref] .

Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua · Type IIA Description: the Generating Function of the Noether–Lefschetz Numbers · 0.97

Cites it as background 7 papers

Following the reviews of semi-stable degenerations and Kulikov models in [ref] , let us discuss how the degenerate K3-fibers fit in Kulikov's classification.

The Asymptotic Weak Gravity Conjecture in M-theory · Fibrations with Degenerations · 0.95
Morally, this is a question of whether one of the curves in the degenerate fibers can be shrunk to zero size, leading to a true $ℙ^1$-bundle[Note that the study of $ℙ^1$-fibrations and their degenerations in this context is intrinsically linked to the study of $K3$-fiber degenerations in F-theory [ref] .].

$\mathbb{P}^1$-fibrations in F-theory and String Dualities · Conic bundles · 0.83
A general discussion of reducible K3 fibers, their monodromies, and the relation to NS5-branes can be found in Ref. [ref] .

NS5-Branes and Line Bundles in Heterotic/F-Theory Duality · Singularities and small instantons in 6d · 0.90

What it cites · 24 sentences without a confident label

Builds on 1 paper

This is a generalization of the scaling in [ref] .

More on Dimension-4 Proton Decay Problem in F-theory -- Spectral Surface, Discriminant Locus and Monodromy · Lg degeneration of Lg-elliptic K3 surfaces · 1.00

Cites as background 6 papers

For other aspects of hypermultiplet moduli map, see e.g. [ref] and references therein.

Heterotic-Type II duality in the hypermultiplet sector · Lg degeneration of Lg-elliptic K3 surfaces · 0.95
For other aspects of hypermultiplet moduli map, see e.g. [ref] and references therein.

Heterotic-type II duality in twistor space · Lg degeneration of Lg-elliptic K3 surfaces · 0.95
For other aspects of hypermultiplet moduli map, see e.g. [ref] and references therein.

Instantons, Hypermultiplets and the Heterotic String · Lg degeneration of Lg-elliptic K3 surfaces · 0.95

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