Topological Strings And (Almost) Modular Forms

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The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group {Lambda}, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H{sup 3}(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under {Lambda}. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local Calabi-Yau ... continued below

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Aganagic, Mina; Bouchard, Vincent & Klemm, Albrecht May 4, 2007.

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The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group {Lambda}, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H{sup 3}(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under {Lambda}. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local Calabi-Yau manifolds giving rise to Seiberg-Witten gauge theories in four dimensions and local IP{sub 2} and IP{sub 1} x IP{sub 1}. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for Gromov-Witten invariants of the orbifold C{sub 3}/ZZ{sub 3}.

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  • Journal Name: Communications in Mathematical Physics; Journal Volume: 277; Journal Issue: 3; Related Information: Journal Publication Date: 02/2008

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  • Report No.: LBNL--61944
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 928577
  • Archival Resource Key: ark:/67531/metadc902670

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  • May 4, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 2, 2016, 3:48 p.m.

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Aganagic, Mina; Bouchard, Vincent & Klemm, Albrecht. Topological Strings And (Almost) Modular Forms, article, May 4, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc902670/: accessed October 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.