Integrability of the holomorphic anomaly equations

Haghighat, Babak; Klemm, Albrecht; Rauch, Marco

doi:10.1088/1126-6708/2008/10/097

Cited by 83 publications

(186 citation statements)

References 36 publications

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“…The higher N corrections are related to these periods by a recursive procedure, which amounts to integration of the loop equations of the matrix model [19,30]. In (16), X,Y are C * variables, and (16) is the B-model mirror curve of the local Calabi-Yau geometry …”

Section: The Geometry Of the Abjm Theorymentioning

confidence: 99%

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Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Klemm

Mariño

Soroush

2013

Zeitschrift Für Naturforschung A

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159

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The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the WentzelKramer-Brillouin expansion. We present explicit results for the vevs of 1/6 and the 1/2 BogomolnyiPrasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the 't Hooft expansion.

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Section: The Geometry Of the Abjm Theorymentioning

confidence: 99%

“…can be identified with an algebraic submanifold of the complex deformation space of (16). This submanifold is simply given by…”

Section: The Geometry Of the Abjm Theorymentioning

confidence: 99%

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Klemm

Mariño

Soroush

2013

Zeitschrift Für Naturforschung A

Self Cite

159

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“…(7)(8)(9)(10)(11). It should be noted that the discussion in the following holds in general and can be applied both for compact and local models.…”

Section: Constructing the Propagatorsmentioning

confidence: 99%

“…At the time of finishing this work a paper appeared [11] where the authors also use the polynomial construction to study local models.…”

Section: Introductionmentioning

confidence: 99%

Global properties of topological string amplitudes and orbifold invariants

Alim¹,

Länge²,

Mayr³

2010

J. High Energ. Phys.

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We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for

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“…Furthermore we reproduce the closed invariants of [269] for the two P 1 -classes for zero brane winding m = 0. First we identify in the polyhedron (C.17) the vector ℓ (4) as corresponding to the brane vector.…”

Section: C2 Further Examples Of Fourfoldsmentioning

confidence: 99%

Holomorphic couplings in non‐perturbative string compactifications

Klevers

2011

Fortschritte der Physik

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In this review article 1 we present an analysis of several aspects of four-dimensional, nonperturbative N = 1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N = 1 effective action, most prominently the superpotential W . This article is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we perform exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefoldẐ 3 , that is canonically constructed from the original fivebrane and the Calabi-Yau threefold Z 3 via a blow-up. We use the blow-up threefoldẐ 3 to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpretẐ 3 as a flux compactification geometrically dual to the original five-brane by defining an SU (3)-structure onẐ 3 , that is generated dynamically by the five-brane backreaction.

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Integrability of the holomorphic anomaly equations

Cited by 83 publications

References 36 publications

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Global properties of topological string amplitudes and orbifold invariants

Holomorphic couplings in non‐perturbative string compactifications

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