Article

Exact Results in ABJM Theory from Topological Strings

Journal of High Energy Physics (Impact Factor: 6.22). 12/2009; 2010(6). DOI: 10.1007/JHEP06(2010)011
Source: arXiv

ABSTRACT Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and Trancanelli Comment: 18 pages, two figures, small misprints corrected and references added, final version to appear in JHEP

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    ABSTRACT: The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.
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    03/2012, Degree: PhD, Supervisor: Luca Griguolo

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