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Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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Unquenched flavor and tropical geometry in strongly coupled Chern–Simons–matter theories
, 2011
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The partition function of ABJ theory
, 2013
"... We study the partition function of the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N1)×U(N2) lens space matrix model exactly. The result can be expressed as a product of qdef ..."
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We study the partition function of the N = 6 supersymmetric U(N1)k × U(N2)−k ChernSimonsmatter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N1)×U(N2) lens space matrix model exactly. The result can be expressed as a product of qdeformed Barnes Gfunction and a generalization of multiple qhypergeometric function. The ABJ partition function is then obtained from the lens space partition function by analytically continuing N2 to −N2. The answer is given by min(N1, N2)dimensional integrals and generalizes the “mirror description ” of the partition function of the ABJM theory, i.e. the N = 6 supersymmetric U(N)k × U(N)−k CSM theory. Our expression correctly reproduces perturbative expansions and vanishes for N1 − N2 > k in line with the conjectured supersymmetry breaking, and the Seiberg duality is explicitly checked for a class of nontrivial examples.
Instanton Effects in ABJM Theory from Fermi Gas Approach, JHEP 1301 (2013) 158, [arXiv:1211.1251
 Instanton Bound States in ABJM Theory, JHEP 1305 (2013) 054, [arXiv:1301.5184
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Partition Functions of Superconformal ChernSimons Theories from Fermi Gas Approach
, 2014
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Lightlike polygonal Wilson loops in 3d ChernSimons and ABJM theory”, JHEP 1008, 032
 in ChernSimons Matter Theories”, JHEP 1106, 118 (2011), arxiv:1103.3675. • K. Wiegandt, “Equivalence of Wilson Loops in N = 6 super ChernSimons matter theory and N = 4 SYM Theory”, Phys.Rev. D84
, 2010
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ABJM Wilson loops in the Fermi . . .
, 2013
"... The matrix model of ABJM theory can be formulated in terms of an ideal Fermi gas with a nontrivial oneparticle Hamiltonian. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statisticalmechanical problem. This makes it possible to calculate these v ..."
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The matrix model of ABJM theory can be formulated in terms of an ideal Fermi gas with a nontrivial oneparticle Hamiltonian. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statisticalmechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern–Simons coupling, by using the WKB expansion. We present explicit results for the vevs of 1/6 and the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.