Les Houches lectures on matrix models and topological strings
By Marcos Mariño. 2004
234 citations recorded by the source corpus.
In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model technology and then we focus on type B topological strings. We present the main results of Dijkgraaf and Vafa describing the spacetime string dynamics on certain Calabi-Yau backgrounds in terms of matrix models, and we emphasize the connection to geometric transitions and to large N gauge/string duality. We also use matrix model technology to analyze large N Chern-Simons theory and the Gopakumar-Vafa transition.
Subfields: Algebra and Number Theory, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/912b9c418eaa7d8154722a6f6f95e9e9c33efceb
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In Algebra and Number Theory
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Citations in the corpus
- The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, methodology): “Again, this procedure is somewhat standard, and a review may be found in [37].”
- Lectures on black holes, topological strings and quantum attractors (2006, background): “Other valuable reviews of topological string theory include [56, 57, 58, 59, 60].”
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, background): “(7.3) { 45 { is the Vandermonde determinant (6.33) for the group U(N). The integral (7.1) is typically obtained as a reduction to eigenvalues of integrals over the space of N NHermitian matrices, see [29, 74] for more details. We want to study Zin the so-called ’t Hooft limit, in which gs!0; N!1; (7”
- Exact results in ABJM theory from topological strings (2009, background): “Notice that, if t2 = 0, one has β = 2, α = 4e t − 2, and ρ1(x) becomes the density of eigenvalues for the matrix model of Chern–Simons theory on S3 [29]”
- From Weak to Strong Coupling in ABJM Theory (2010, background): “Indeed, the VEVs 〈TrR U 〉 for the Chern–Simons matrix model on S3 are proportional to quantum dimensions (see for example [21]): 〈TrR U 〉 = qκR/2+ dimq(R).”
- Invariants of algebraic curves and topological expansion (2007, methodology): “Let us also mention that other methods were invented using orthogonal polynomials [67] (only in the case were the formal integral comes from an actual convergent integral), or topological string theory methods [11,22,65] using the so-called holomorphic anomaly equations.”
- Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “It gives the genus expansion of the c = 1 string at the self-dual radius (see for example [84]), and it also appears in the asymptotic 1/N expansion of the partition function of the Gaussian matrix model (see for example [92]).”