Summing up all genus free energy of ABJM matrix model

By H. Fuji, S. Hirano, Sanefumi Moriyama. 2011

203 citations recorded by the source corpus.

The localization technique allows us to compute the free energy of the U(N)k × U(N)−k Chern-Simons-matter theory dual to type IIA strings on AdS4 × CP3 from weak to strong ’t Hooft coupling λ = N/k at finite N, as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large ’t Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up allthe1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form — the Airy function, $ {\text{Ai}}\left( {{{\left( {{{{\pi {k^2}}} \left/ {{\sqrt {2} }} \right.}} \right)}^{{{2} \left/ {3} \right.}}}{\lambda_{\text{ren}}}} \right) $, with the renormalized ’t Hooft coupling λren.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/585d5de5e6d111eb390c7f83903c9640e45a62e9

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Citations in the corpus

Instanton bound states in ABJM theory (2013, methodology): “After that, it was shown in [8] that the all-genus summation”
A one-loop test of quantum supergravity (2012, methodology): “For these theories, the partition function at all orders in 1/N was computed in [3, 4] by generalizing earlier work in [5, 6, 7, 8].”
Exact results on the ABJM Fermi gas (2012, methodology): “In [15, 17], it was shown that the ABJM partition function is written in terms of the Airy function if one neglects the instanton corrections.”
Instanton effects in ABJM theory from Fermi gas approach (2012, background): “There is much progress in this matrix model including the derivation of the degree of freedom N [6] expected from the AdS/CFT correspondence [7] and its perturbative completion by the Airy function [8].”
Non-perturbative effects and the refined topological string (2013, background): “15), the perturbative piece J (p)(μ, k) leads to the Airy function result for Z(N, k) first obtained in [25].”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “[33] the genus expansion at strong ’t Hooft coupling has been considered and a resummed form was obtained in terms of the Airy function by using the holomorphic anomaly equation [36].”
ABJM theory as a Fermi gas (2011, methodology): “Finally, building on the results of [5, 8], it was shown in [9] that, once worldsheet instantons are discarded, the full free energy of the ABJM matrix model is given by an Airy function.”