Solving the Topological String on K3 Fibrations

Albrecht Klemm; Babak Haghighat

RECORD

Solving the Topological String on K3 Fibrations

Babak Haghighat, Albrecht Klemm

High Energy Physics - Theory · Submitted 4 Aug 2009

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

The authors' main claim We present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,953 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space. In particular we focus on K3-fibrations where due to heterotic type II duality the topological invariants in the fibre direction are encoded in certain modular forms. The formalism employed provides holomorphic expansions of topological string amplitudes everywhere in moduli space.

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 present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space.	contribution 0.92	0.95	0.53	asserted 1.00
s1	In particular we focus on K3-fibrations where due to heterotic type II duality the topological invariants in the fibre direction are encoded in certain modular forms.	contribution 0.72	0.29	0.17	asserted 1.00
s2	The formalism employed provides holomorphic expansions of topological string amplitudes everywhere in moduli space.	result 0.58	0.86	0.27	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space. In particular we focus on K3-fibrations where due to heterotic type II duality the topological invariants in the fibre direction are encoded in certain modular forms. The formalism employed provides holomorphic expansions of topological string amplitudes everywhere in moduli space.

Human review

How Pith checks papers → · Full audit of this paper →

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

Quantum geometry of elliptic Calabi-Yau manifolds
hep-th 2012-05 conditional novelty 6.0 of 10

A holomorphic anomaly equation is proposed for topological strings on elliptic Calabi-Yau threefolds and checked, for up to three D4-branes on the rational elliptic surface, against independent sheaf-counting computations.
Direct integration for general Omega backgrounds
hep-th 2010-09 conditional novelty 6.0 of 10

A generalized holomorphic anomaly equation plus a conifold gap condition is shown sufficient to compute refined topological string amplitudes on several non-compact Calabi-Yau spaces, matching independent refined-vert...

How the literature uses it

13 arXiv papers cite this in 23 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 · 19 sentences without a confident label

Cites it as support 1 paper

It was furthermore shown in explicit examples [ref] that there are choices of $ℰ^zz,ℰ^z,ℰ$ such that $h^zz_z,h^z_z,h_zz,h_z,h_zzzz$ are rational functions in $z$ of the form $p(z)/Δ$ where $Δ$ is the discriminant, and $p(z)$ is a polynomial in the algebraic complex structure coordinates.

Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings · Polynomial ring of sections in arbitrary coordinates · 0.97

Cites it as background 3 papers

Since then, there has been steady progress in physics on the modularity conjecture [ref] .

Gromov-Witten Theory of Quotient of Fermat Calabi-Yau varieties · Introduction · 0.91
Much more general examples have been discussed in [ref] [ref] .

Direct integration for general Omega backgrounds · Heterotic/Type II duality · 0.80
This method has been developed in the context of topological string theory in [ref] .

Direct Integration and Non-Perturbative Effects in Matrix Models · Introduction · 0.94

What it cites · 54 sentences without a confident label

Uses the method or tool of 7 papers

In this section we want to outline a method of solution of the B-model higher genus amplitudes using the holomorphic anomaly equations [ref] , the modular properties of the $F_g$ [ref] and boundary conditions in particular the gap conditions of [ref] .

Polynomial Structure of the (Open) Topological String Partition Function · Solving the holomorphic anomaly equations · 0.96
In this section we want to outline a method of solution of the B-model higher genus amplitudes using the holomorphic anomaly equations [ref] , the modular properties of the $F_g$ [ref] and boundary conditions in particular the gap conditions of [ref] .

Topological String Partition Functions as Polynomials · Solving the holomorphic anomaly equations · 0.96
In this section we want to outline a method of solution of the B-model higher genus amplitudes using the holomorphic anomaly equations [ref] , the modular properties of the $F_g$ [ref] and boundary conditions in particular the gap conditions of [ref] .

Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions · Solving the holomorphic anomaly equations · 0.96

Uses data or values from 1 paper

The analysis was done in [ref] and the result is the following set of boundary divisors: [equation]

Mirror Symmetry for Two Parameter Models -- I · The Moduli Space of the Mirror · 0.92

Cites as background 7 papers

In this section we want to give an overview of the moduli Space of K3 fibrations as presented in [ref] .

Mirror Symmetry for Two Parameter Models -- I · Moduli Space of K3 Fibrations · 1.00
Recent progress in the computation of topological string amplitudes to higher genus on compact Calabi-Yau manifolds [ref] [ref] [ref] raises the question of integrability of the closed topological string on these backgrounds.

Topological Strings on Grassmannian Calabi-Yau manifolds · Introduction · 0.87
Recent progress in the computation of topological string amplitudes to higher genus on compact Calabi-Yau manifolds [ref] [ref] [ref] raises the question of integrability of the closed topological string on these backgrounds.

Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds · Introduction · 0.87

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.