Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories

By Marcos Mariño. 2011

222 citations recorded by the source corpus.

In these lectures, I give a pedagogical presentation of some of the recent progress in supersymmetric Chern–Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N3/2 behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals and large N techniques in matrix models.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0aa01955f765552e3d83eb2879c2cf7a93718fcf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

A one-loop test of quantum supergravity (2012, background): “the path integral still includes a factor of 1/vol(H), where H is the subgroup of gauge transformations generated by zero modes (see [11], section 3.”
ABJM theory as a Fermi gas (2011, background): “In the last year, many results have been obtained for these matrix models, providing precision tests of the AdS4/CFT3 correspondence as well as beautiful field-theoretical results on supersymmetric CSM theories (see [7] for a review and a list of references).”
F-theorem without supersymmetry (2011, unknown): “This result agrees with earlier work [55].”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, unknown): “For a nice review, see [27].”
Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “31) have their counterparts in matrix models and topological string theory [40, 41] and 4d gauge theory compactified on R3 × S1 [17].”
Summing up all genus free energy of ABJM matrix model (2011, methodology): “As demonstrated by Drukker, Mariño, and Putrov [9, 11, 10], the free energy can be calculated for arbitrary ’t Hooft coupling λ and order by order in the 1/N expansion.”
Interpolating between a and F (2014, background): “Indeed, the supersymmetric Lagrangian for a free chiral multiplet with non-canonical dimension ∆ is given by [18, 19, 91]”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “and in principle it can be computed by standard perturbative techniques (see [96] for a review).”
Localization on Hopf surfaces (2014, background): “Let us discuss the first condition, while we will deal with the second condition later [33, 34].”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “Most of the examples studied in the last few years are not topologically twisted [2] (see [3] for a nice review”