Chern-Simons Matrix Models and Unoriented Strings

Abstract

For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F_{1}(S)=\pm{1/4}\frac{\del F_{0}(S)}{\del S}. Motivated by the fact that this relationship does not hold for Chern-Simons theory on S^{3}, we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F_{1} is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory.

28 pages, 2 figures V2: re-organised for clarity, results unchanged

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Cited by in corpus (11)

• Les Houches lectures on matrix models and topological strings
• Soft matrix models and Chern-Simons partition functions
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• The Spectral Curve of the Lens Space Matrix Model
• Characterisation of a CMOS Active Pixel Sensor for use in the TEAM Microscope
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Large N Duality, Lens Spaces and the Chern-Simons Matrix Model
• Bubbling Calabi-Yau geometry from matrix models
• Chern-Simons matrix model for local conifold
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Subleading Corrections in N=3 Gaiotto-Tomasiello Theory