Topological Strings, TwoDimensional YangMills Theory and ChernSimons Theory on Torus Bundles
Caporaso, N, Cirafici, M, Griguolo, L, Pasquetti, S, Seminara, D and Szabo, RJ (2006) Topological Strings, TwoDimensional YangMills Theory and ChernSimons Theory on Torus Bundles Adv.Theor.Math.Phys., 12 (5). pp. 9811058.

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Abstract
We study the relations between twodimensional YangMills theory on the torus, topological string theory on a CalabiYau threefold whose local geometry is the sum of two line bundles over the torus, and ChernSimons theory on torus bundles. The chiral partition function of the YangMills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use YangMills theory as an efficient tool for the computation of GromovWitten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the GopakumarVafa invariants, whose integrality gives a nontrivial confirmation of the conjectured nonperturbative relation between twodimensional YangMills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the DonaldsonThomas theory of the CalabiYau background. We match the instanton representation of YangMills theory on the torus with the nonabelian localization of ChernSimons gauge theory on torus bundles over the circle. We also comment on how these results can be applied to the computation of exact degeneracies of BPS black holes in the local CalabiYau background.
Item Type:  Article  

Divisions :  Faculty of Engineering and Physical Sciences > Mathematics  
Authors : 


Date :  19 September 2006  
Uncontrolled Keywords :  hepth, hepth, math.AG  
Related URLs :  
Additional Information :  Published version can be found here: http://arxiv.org/abs/hepth/0609129  
Depositing User :  Symplectic Elements  
Date Deposited :  22 Jan 2016 09:41  
Last Modified :  31 Oct 2017 17:53  
URI:  http://epubs.surrey.ac.uk/id/eprint/809370 
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