Mirrorfolds with K3 Fibrations

Shinsuke Kawai; Yuji Sugawara

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Mirrorfolds with K3 Fibrations

Shinsuke Kawai, Yuji Sugawara

High Energy Physics - Theory · Submitted 7 Nov 2007

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

The authors' main claim Starting with arbitrary (compact or non-compact) Gepner models for the $K3$ fiber, we construct modular invariant partition functions of general mirrorfold models.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.69 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT). These models are defined as `interpolating orbifolds' of $K3 \times S^1$ by the mirror transformation acting on the $K3$ fiber combined with the half-shift on the $S^1$-base. They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called `mirrorfolds'. Starting with arbitrary (compact or non-compact) Gepner models for the $K3$ fiber, we construct modular invariant partition functions of general mirrorfold models. In the case of compact $K3$ fiber the mirrorfolds only yield non-supersymmetric string vacua. They exhibit IR instability due to winding tachyon condensation which is similar to the Scherk-Schwarz type circle compactification. When the fiber SCFT is non-compact (say, the ALE space in the simplest case), on the other hand, both supersymmetric and non-supersymmetric vacua can be constructed. The non-compact non-supersymmetric mirrorfolds can get stabilised at the level of string perturbation theory. We also find that in the non-compact supersymmeric mirrorfolds D-branes are {\em always} non-BPS. These D-branes can get stabilized against both open- and closed-string marginal deformations.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT).	contribution 1.00	0.91	0.10	asserted 1.00
s1	These models are defined as `interpolating orbifolds' of $K3 \times S^1$ by the mirror transformation acting on the $K3$ fiber combined with the half-shift on the $S^1$-base.	method 0.61	0.49	0.08	asserted 1.00
s2	They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called `mirrorfolds'.	background 0.56	0.31	0.10	hedged possibility 0.79
s3	Starting with arbitrary (compact or non-compact) Gepner models for the $K3$ fiber, we construct modular invariant partition functions of general mirrorfold models.	method 0.70	0.95	0.10	asserted 1.00
s4	In the case of compact $K3$ fiber the mirrorfolds only yield non-supersymmetric string vacua.	result 0.98	0.82	0.12	asserted 1.00
s5	They exhibit IR instability due to winding tachyon condensation which is similar to the Scherk-Schwarz type circle compactification.	result 0.95	0.80	0.09	asserted 1.00
s6	When the fiber SCFT is non-compact (say, the ALE space in the simplest case), on the other hand, both supersymmetric and non-supersymmetric vacua can be constructed.	result 0.99	0.85	0.14	asserted 0.81
s7	The non-compact non-supersymmetric mirrorfolds can get stabilised at the level of string perturbation theory.	result 1.00	0.82	0.12	hedged possibility 0.78
s8	We also find that in the non-compact supersymmeric mirrorfolds D-branes are {\em always} non-BPS.	result 1.00	0.92	0.13	asserted 1.00
s9	These D-branes can get stabilized against both open- and closed-string marginal deformations.	result 1.00	0.87	0.12	asserted 0.76

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT). These models are defined as `interpolating orbifolds' of $K3 \times S^1$ by the mirror transformation acting on the $K3$ fiber combined with the half-shift on the $S^1$-base. They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called `mirrorfolds'. Starting with arbitrary (compact or non-compact) Gepner models for the $K3$ fiber, we construct modular invariant partition functions of general mirrorfold models. In the case of compact $K3$ fiber the mirrorfolds only yield non-supersymmetric string vacua. They exhibit IR instability due to winding tachyon condensation which is similar to the Scherk-Schwarz type circle compactification. When the fiber SCFT is non-compact (say, the ALE space in the simplest case), on the other hand, both supersymmetric and non-supersymmetric vacua can be constructed. The non-compact non-supersymmetric mirrorfolds can get stabilised at the level of string perturbation theory. We also find that in the non-compact supersymmeric mirrorfolds D-branes are {\em always} non-BPS. These D-branes can get stabilized against both open- and closed-string marginal deformations.

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References

Forward citations

Cited by 3 Pith papers

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

The Geometry, Branes and Applications of Exceptional Field Theory
hep-th 2020-06 accept novelty 2.0 of 10

Exceptional field theory recasts the maximal supergravities as a single extended geometry whose local symmetry is the exceptional U-duality group Ed(d), with extra coordinates conjugate to brane winding modes.
Non-geometric backgrounds in string theory
hep-th 2018-11 accept

The review maps how T-duality, generalised geometry, and flux compactifications describe string backgrounds that cannot be given an ordinary Riemannian geometry.
Duality Symmetric String and M-Theory
hep-th 2013-06 accept

The paper is a review that connects the doubled worldsheet, Double Field Theory, and exceptional generalised geometry as one program for making T- and U-duality manifest.

How the literature uses it

14 arXiv papers cite this in 22 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Builds on it 1 paper

The idea of T-folds can be naturally extended to compactifications with U-duality twists (U-folds) [ref] and, given the understanding of mirror symmetry as T-duality [ref] , may allow mirror-folds for Calabi-Yau compactifications [ref] .

T-duality Invariant Approaches to String Theory · T-folds · 0.82

Uses its method or tool 1 paper

We can determine them in a way parallel to that presented in [ref] .

Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds · Concrete Examples : Gepner Construction · 0.98

Compares with it 1 paper

Previously Kawai et Sugawara have considered in [ref] K3 mirror-folds with monodromies that, at least when the fiber is compact, break all supersymmetry; in the present work, we consider in contrast monodromies that preserve 8 supersymmetries, i.e. which preserve a quarter of the 32 supersymmetries of the type IIA string, or a half of the 16 supersymmetries of type IIA compactified on $K3$.

Non-geometric Calabi-Yau Backgrounds and K3 automorphisms · Introduction · 0.93

Cites it as background 7 papers

The idea of a Mirror-fold is not new (see, for example, [ref] ) and in [ref] a CFT for the interpolating orbifold corresponding to a Mirror-fold was explicitly constructed.

N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory · Mirror-folds and Non-Geometric Backgrounds with $𝒬_i^A$ Flux · 0.92
Such T-fold CFTs have been studied e.g. in [ref] .

Lie algebra lattices and strings on T-folds · Introduction · 0.86
To our knowledge, analogous supersymmetric constructions in type IIA/IIB superstrings have not been considered yet.[Different constructions of non-supersymmetric asymmetric models were considered in [ref] .]

Asymmetric Gepner models in type II · Introduction · 0.81

What it cites · 36 sentences without a confident label

Uses the method or tool of 1 paper

A way to circumvent this problem is to focus only on the propagating degrees of freedom, by considering the partition function per unit volume as discussed in [ref] ; [equation] Note that the second term $Z_dis$ drops after divided by the infinite volume factor $V$.

SL(2,R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds · Non-SUSY Vacua : Symmetric Modular Invariants · 0.92

Cites as background 5 papers

In such models the moduli space of the fibre, when going around non-trivial cycles on the base manifold, picks up monodromies in general; for this reason these string vacua are often called `monodrofolds.' In particular, monodrofolds constructed from T-duality transformations are called `T-folds' [ref] .

A Geometry for Non-Geometric String Backgrounds · Introduction and Summary · 0.98
By now, several models of T-folds have been analysed using CFT [ref] .

Nongeometry, Duality Twists, and the Worldsheet · Introduction and Summary · 0.85
By now, several models of T-folds have been analysed using CFT [ref] .

Worldsheet CFTs for Flat Monodrofolds · Introduction and Summary · 0.85

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