On Chern-simons Matrix Models
نویسنده
چکیده
The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold M can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simons matrix integral for Seifert spheres and the trivial connection.
منابع مشابه
Matrix Model as a Mirror of Chern-Simons Theory
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological...
متن کاملChern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermi...
متن کاملMulti-Matrix Models and Tri-Sasaki Einstein Spaces
Localization methods reduce the path integrals in N ≥ 2 supersymmetric Chern-Simons gauge theories on S to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the N = 6 superconformal U(N) × U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining in particular the N scaling of the free energy. We study a class of p-matrix integrals desc...
متن کاملScattering in Mass-Deformed N>=4 Chern-Simons Models
We investigate the scattering matrix in mass-deformed N ≥ 4 Chern– Simons models including as special cases the BLG and ABJM theories of multiple M2 branes. Curiously the structure of this scattering matrix in three spacetime dimensions is equivalent to (a) the two-dimensional worldsheet matrix found in the context of AdS/CFT integrability and (b) the R-matrix of the one-dimensional Hubbard mod...
متن کاملThe Chern-Simons One-form and Gravity on a Fuzzy Space
The one-dimensional N ×N -matrix Chern-Simons action is given, for large N and for slowly varying fields, by the (2k + 1)-dimensional Chern-Simons action SCS , where the gauge fields in SCS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by t...
متن کامل