On N=1 Mirror Symmetry for Open Type II Strings

P. Mayr; W. Lerche

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On N=1 Mirror Symmetry for Open Type II Strings

W. Lerche, P. Mayr

High Energy Physics - Theory · Submitted 13 Nov 2001

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

The authors' main claim The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone. Applications to a variety of D-brane geometries are described in some detail.

background contribution method result interpretation main claim

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 the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds.	contribution 0.99	0.88	0.09	asserted 0.92
s1	Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals.	method 0.90	0.70	0.06	asserted 1.00
s2	The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume.	result 0.72	0.78	0.38	asserted 1.00
s3	A gauged linear sigma model for the combined open-closed string system is also given.	method 0.56	0.88	0.05	asserted 1.00
s4	It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone.	method 0.85	0.76	0.06	asserted 0.94
s5	Applications to a variety of D-brane geometries are described in some detail.	contribution 0.94	0.80	0.07	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.79 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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The paper

Original abstract

We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone. Applications to a variety of D-brane geometries are described in some detail.

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References

Forward citations

Cited by 7 Pith papers

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

Hodge-theoretic Open/Closed Correspondence
math.AG 2025-07 conditional novelty 7.0 of 10

The relative periods and mixed Hodge structures of an open toric Calabi-Yau 3-orbifold with a brane agree, up to a Tate twist, with the periods and mixed Hodge structures of a closed toric Calabi-Yau 4-orbifold.
Remodeling the B-model
hep-th 2007-09 accept novelty 7.0 of 10

A recursive residue calculus on the mirror curve in C* x C* generates all open and closed B-model topological string amplitudes, checked against the topological vertex and against Chern-Simons Wilson loops in lens spaces.
Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions
hep-th 2026-03 unverdicted novelty 6.0 of 10

Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.
Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String
hep-th 2010-08 conditional novelty 6.0 of 10

Instanton partition functions with a surface operator agree, order by order in the instanton expansion, with Liouville correlators carrying a degenerate insertion and with open topological string amplitudes on local H...
Computing Brane and Flux Superpotentials in F-theory Compactifications
hep-th 2009-09 conditional novelty 6.0 of 10

An explicit Calabi-Yau fourfold computation shows that a single four-form flux reproduces the full D5-brane disk instanton superpotential of local P2 in a local limit.

Show 2 more citing papers

Open string amplitudes and large order behavior in topological string theory
hep-th 2006-12 conditional novelty 6.0 of 10

Matrix-model loop equations, run on a spectral curve read off from the disk amplitude, reproduce known open topological string amplitudes on toric Calabi-Yau manifolds and give the D-brane instanton action that sets t...
Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
hep-th 2006-10 unverdicted

A comprehensive pedagogical review of four-dimensional orientifold and flux compactifications with D-branes, assembling model-building rules, effective-action methods, and statistical vacuum counts.

How the literature uses it

30 arXiv papers cite this in 64 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 · 48 sentences without a confident label

Uses its method or tool 3 papers

(ii) We use the approach in Graber-Zaslow [ref] to prove the mirror conjecture on disk invariants in [ref] for any smooth semi-projective toric Calabi-Yau 3-folds.

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds · Summary of results · 0.93
The closed and open mirror maps are given by [ref] , [equation] where $X=X(x)$ is the open string moduli on the A model side.

Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String · Toric brane on local Hirzebruch surface $K_F_0$: pure $SU(2)$ · 0.80
The open mirror map ([ref]) is given by [ref] [equation] By applying the mirror maps ([ref]) and ([ref]) to ([ref]), we can obtain the annulus amplitude $A_A(X_1,X_2)$ on $K_dP_5$.

Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model · Examples · 0.82

Compares with it 3 papers

The computations of [ref] agree with Mayr's calculations using differential equations [ref] , a method further developed in [ref] .

The proper Landau-Ginzburg potential is the open mirror map · Steps of the proof and auxiliary results · 0.93
In Phase III, when $f=0$ we have [equation] which agrees with [ref] .

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds · Mirror Formula: · 0.99
An “open/closed relation” of somewhat different flavor is present in open GW theory of toric Calabi-Yau 3-folds with respect to Aganagic-Vafa type Lagrangian branes; see [ref] .

Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds · Outline of methods · 0.85

Cites it as support 1 paper

Important circumstantial evidence for the open-string/fourfold duality approach [ref] advocated in this paper is the identical integral structure of the generating functions.

Computing Brane and Flux Superpotentials in F-theory Compactifications · Basics of enumerative geometry · 0.98

Cites it as background 9 papers

By “open mirror map,” we mean the relation between complex and symplectic open parameters defined by the logarithmic solution to the Picard–Fuchs differential equations of Lerche–Mayr [ref] — see Section [ref].

The proper Landau-Ginzburg potential is the open mirror map · Introduction and Summary · 0.80
We refer the reader to [ref] for a detailed explanation of the extended Picard-Fuchs system.

Topological open strings on orbifolds · The open mirror map · 0.86
It also plays an important role in approaches to open mirror symmetry, including open-closed Picard-Fuchs equations and relative period integrals [ref] .

Moduli Webs and Superpotentials for Five-Branes · Introduction · 0.90

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