c-map as c=1 string

Sergei Alexandrov

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c-map as c=1 string

Sergei Alexandrov

High Energy Physics - Theory · Submitted 20 Jan 2012

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

The authors' main claim We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.29 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. It appears as a particular case of a general relation between the twistor description of four-dimensional quaternionic geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an evidence that the instanton corrections to the c-map metric coming from NS5-branes can be encoded into the Baker-Akhiezer function of the integrable hierarchy.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential.	result 0.86	0.92	0.84	asserted 1.00
s1	It appears as a particular case of a general relation between the twistor description of four-dimensional quaternionic geometries and the Lax formalism for Toda hierarchy.	interpretation 0.92	0.30	0.09	hedged possibility 0.91
s2	Furthermore, we give an evidence that the instanton corrections to the c-map metric coming from NS5-branes can be encoded into the Baker-Akhiezer function of the integrable hierarchy.	result 0.82	0.88	0.16	hedged possibility 0.93

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

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The paper

Original abstract

We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. It appears as a particular case of a general relation between the twistor description of four-dimensional quaternionic geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an evidence that the instanton corrections to the c-map metric coming from NS5-branes can be encoded into the Baker-Akhiezer function of the integrable hierarchy.

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References

Forward citations

Cited by 2 Pith papers

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

Twistor Approach to String Compactifications: a Review
hep-th 2011-11 conditional novelty 5.0 of 10

D-brane and NS5-brane instanton corrections to the hypermultiplet moduli space of type II Calabi-Yau compactifications can be encoded as holomorphic transition functions on a twistor space, with S-duality, mirror symm...
Quantum hypermultiplet moduli spaces in N=2 string vacua: a review
hep-th 2013-04 accept novelty 2.0 of 10

The exact hypermultiplet moduli space metric is encoded in a complex contact structure on twistor space, built from Donaldson-Thomas invariants and constrained by wall-crossing and S-duality.

How the literature uses it

6 arXiv papers cite this in 7 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 · 6 sentences without a confident label

Cites it as background 1 paper

These go by the names of the r-map and c-map, and although they have been known for some time [ref] , they have also seen much recent interest, a small sample of which is given by [ref] .

Non-extremal black holes from the generalised r-map · Introduction · 1.00

What it cites · 54 sentences without a confident label

Uses the method or tool of 1 paper

The most convenient way to describe the dynamics of these free fermions is to use the light-cone coordinates [ref] $=x±p/√(2)$ where $(x,p)$ are the coordinates on the phase space of one fermion.

Time-dependent backgrounds of 2D string theory · Example: MQM with sine-Liouville perturbation · 0.91

Cites as support 1 paper

Indeed, the Heisenberg symmetry mentioned above, in the presence of a non-vanishing NS5-brane charge, becomes equivalent to the quantum torus algebra [ref] .

Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces · Discussion · 0.99

Cites as background 9 papers

In particular, in the $c=1$ string theory with the sine-Liouville perturbation the non-perturbative corrections have been studied in [ref] .[It should be noted that most of the studies of $c=1$ string theory with the sine-Liouville perturbation have been done for arbitrary compactification radius $R$.

Non-Perturbative Effects in Matrix Models and D-branes · Discussion · 0.88
In particular, in the $c=1$ string theory with the sine-Liouville perturbation the non-perturbative corrections have been studied in [ref] .[It should be noted that most of the studies of $c=1$ string theory with the sine-Liouville perturbation have been done for arbitrary compactification radius $R$.

Time-dependent backgrounds of 2D string theory: Non-perturbative effects · Discussion · 0.88
On the other hand, the integrability becomes transparent in its matrix model description in terms of Matrix Quantum Mechanics (see [ref] for a review).

Matrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial Backgrounds · Example: MQM with sine-Liouville perturbation · 0.89

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