Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

By Masanori Hanada, Masazumi Honda, Yoshinori Honma, Jun Nishimura, Shotaro Shiba, Yutaka Yoshida. 2012

144 citations recorded by the source corpus.

A bstractWe show that the ABJM theory, which is an $ \mathcal{N} = {6} $ superconformal U(N) × U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS4/CFT3 duality at the quantum level. Here we calculate the free energy, and confirm the N3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/13404ab1ff5cd410f97d690f294dabc86c61737d

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In Nuclear and High Energy Physics

Citations in the corpus

From Weak to Strong Coupling in ABJM Theory (2010, unknown): “It was determined numerically in [48].”
Topological Strings from Quantum Mechanics (2014, background): “In ABJM theory there is a proposal for this function based on the resummation of the constant map contribution to the topological string free energies [61].”
Instanton effects in ABJM theory from Fermi gas approach (2012, background): “9), and Ak was conjectured in [9, 19] as Ak = − ζ(3) 8π2 k(2) + 1 6 log 4π k + 2ζ ′(−1)− 1 3 ∫ ∞”
Exact results on the ABJM Fermi gas (2012, background): “3) In [31], it was conjectured that this function has the following integral expression, which should be valid for arbitrary k, A(k) = 1 2 log 2− ζ(3) 8π2 k(2) − 1 6 log k + 1 6 log (π 2 )”
ABJM theory as a Fermi gas (2011, methodology): “We would like to thank the authors of [50] for informing us of their result prior to publication, which prompted us to correct a minor sign error in the calculation of (5.”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, unknown): “This was corrected in [76].”
A one-loop test of quantum supergravity (2012, background): “1) is independent of N, but it is a non-trivial function of ka and Nfa (see [4, 9] for explicit results on this coefficient in ABJM theory).”
Instanton bound states in ABJM theory (2013, background): “The small k expansion of A(k) was first computed in [9], and then its exact form was proposed in [19].”