Global properties of topological string amplitudes and orbifold invariants

Alim, Murad; Länge, Jean Dominique; Mayr, Peter

doi:10.1007/jhep03(2010)113

Cited by 24 publications

(61 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A significant step towards efficiently computing the topological 1/N expansion of multi-cut models was very recently given in [35,36], building on [37,38], and opening way to a large-order analysis, and this is a subject we hope to return in the future. This would generalize the one-cut study performed in [15] and would also have direct applications in topological string theory on toric Calabi-Yau manifolds.…”

Section: Discussionmentioning

confidence: 99%

Multi-instantons and multicuts

Mariño¹,

Schiappa²,

Weiss³

2009

Journal of Mathematical Physics

112

View full text Add to dashboard Cite

Abstract:We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painlevé I equation.

show abstract

Section: Discussionmentioning

confidence: 99%

Multi-instantons and multicuts

Mariño¹,

Schiappa²,

Weiss³

2009

Journal of Mathematical Physics

112

View full text Add to dashboard Cite

show abstract

“…The purely holomorphic part of the construction as well as the coefficients of the monomials would be rational functions in the algebraic moduli, this was further discussed in Refs. [ALM10,Hos08].…”

Section: Polynomial Structurementioning

confidence: 99%

“…The freedom in choosing the generators S ij , S i , S was discussed in Ref. [ALM10,Hos08] and translates here to a freedom of adding holomorphic sections E ij , E i , E of L −2 ⊗ Sym m T M with m = 2, 1, 0, respectively to the generators as follows:…”

Section: Special Polynomial Ringsmentioning

confidence: 99%

Gauss–Manin Connection in Disguise: Calabi–Yau Threefolds

Alim

Movasati

Scheidegger

et al. 2016

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

We describe a Lie Algebra on the moduli space of Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions F alg g , g ≥ 1, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

show abstract

“…These formulas are useful [ALM10] in analyzing the degrees of freedom of the holomorphic quantities h…”

mentioning

confidence: 99%

“…Then from Eq. (36) it follows that by choosing vanishing h i j , h i i we can arrange so that the holomorphic limits of S i , S are zero, see [ALM10] for more detailed discussions on this. This sometimes makes the calculations easier when computing the quantity P (g) from recursion.…”

mentioning

confidence: 99%