A Systematic Study on Matrix Models for Chern-Simons-matter Theories

Takao Suyama

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A Systematic Study on Matrix Models for Chern-Simons-matter Theories

Takao Suyama

High Energy Physics - Theory · Submitted 30 Apr 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.74 · mentions code or data availability 0.01.

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We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the 't Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling limit. This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit.	contribution 1.00	0.93	0.06	asserted 0.96
s1	The saddle-point equations for most of such theories can be solved in a systematic way.	method 0.57	0.66	0.07	asserted 0.84
s2	A relation to Fuchsian systems play an important role in obtaining the planar resolvents.	method 0.97	0.52	0.06	asserted 0.99
s3	For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the 't Hooft couplings become large.	result 1.00	0.92	0.21	asserted 1.00
s4	As a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling limit.	result 0.95	0.86	0.22	asserted 0.99
s5	This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory.	interpretation 1.00	0.68	0.39	asserted 0.61
s6	If the gauge group is of the form ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.	result 0.82	0.82	0.05	asserted 0.95

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the 't Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling limit. This implies that many of Chern-Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.

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References

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Exact results on ABJ theory and the refined topological string
hep-th 2014-05 conditional novelty 6.0 of 10

The ABJ partition function on the three-sphere is fixed, order by order in instantons, by the refined topological string on local P1 x P1, extending the ABJM correspondence to nonzero fractional brane number M.
M-theoretic matrix models
hep-th 2014-03 conditional novelty 6.0 of 10

Two matrix models relevant to M-theory and 2d statistical physics are solved exactly in the planar limit, and their M-theory expansions reveal non-perturbative corrections invisible to the 't Hooft expansion.
ABJM Wilson Loops in Arbitrary Representations
hep-th 2013-06 conditional novelty 6.0 of 10

Half-BPS Wilson loop expectation values in ABJM theory obey a Giambelli-type determinant formula in the grand canonical ensemble, reducing every representation to hook representations.
Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
hep-th 2014-07 accept novelty 5.0 of 10

For general N=4 circular-quiver Chern-Simons theories the partition function takes the ABJM Airy form, with an explicit B, a conjectured A for separated quivers, and instanton divergences that cancel in the (2,1) model.

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14 arXiv papers cite this in 21 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Builds on it 1 paper

The analysis in this paper can be extended to a more general family of Chern-Simons-matter theories, based on the results obtained in [ref] .

Supersymmetry Breaking and Planar Free Energy in Chern-Simons-matter Theories · Introduction · 0.93

Cites it as background 9 papers

The planar resolvents for such theories have been investigated in [ref] [ref] [ref] , however, explicit expressions for the resolvents have not been obtained so far except for ABJM theory and ABJ theory [ref] .

Notes on Planar Resolvents of Chern-Simons-matter Matrix Models · Introduction · 0.83
The $S^3$ free energy of the GT theory has been computed in various ways: using resolvents in the 't Hooft limit [ref] ; using the saddle point approximation of a matrix model [ref] and in the Fermi-gas approach in the large-$N$ limit with fixed Chern-Simons levels [ref] .

Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA · Introduction · 0.96
However, if we consider more general M2-brane theory beyond[ For previous studies, see e.g. [ref] in the M-theory limit, [ref] in the 't Hooft limit and [ref] in the Fermi gas approach. ] the ABJ(M) theory, the correspondence to the topological string is rather obscure, and it might be the case that there is no such relation in general.

Exact results on ABJ theory and the refined topological string · Discussions · 0.94

What it cites · 53 sentences without a confident label

Builds on 3 papers

To clarify the situation, it is desired to extend the analysis in [ref] to more general theories.

On Large N Solution of N=3 Chern-Simons-adjoint Theories · Introduction · 0.93
The relation to a Fermi gas can be extended [ref] to various Chern-Simons-matter theories of quiver types originally studied in [ref] .

Multi-Matrix Models and Tri-Sasaki Einstein Spaces · Introduction · 0.92
The relation to a Fermi gas can be extended [ref] to various Chern-Simons-matter theories of quiver types originally studied in [ref] .

ABJM theory as a Fermi gas · Introduction · 0.92

Uses the method or tool of 4 papers

For most of these theories, the Fermi gas approach [ref] results in interacting theories.

ABJM theory as a Fermi gas · Introduction · 0.90
It was found in [ref] that the following ansatz [equation] for the resolvents is quite useful to deal with the logarithmic functions.

On Large N Solution of N=3 Chern-Simons-adjoint Theories · Integral ansatz · 0.96
Using the supersymmetric localization [ref] , $Z(Γ)$ can be written in terms of a finite-dimensional Riemann integral.

Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter · Saddle-point equations for theories in $C$ · 0.89

Compares with 6 papers

The same formula was also derived in [ref] in a different way.

ABJM theory as a Fermi gas · Introduction · 0.90
These theories are rather similar to the Chern-Simons-adjoint theories investigated in [ref] .

On Large N Solution of N=3 Chern-Simons-adjoint Theories · Discussion · 0.96
Similar results were found in [ref] .

Interacting fermions and N=2 Chern-Simons-matter theories · 't Hooft couplings · 0.92

Cites as background 14 papers

In this limit, one finds a relation to M-theory on AdS$_4×S^7/ℤ_k$ [ref] in a quite similar way to the well-studied AdS$_5$/CFT$_4$ correspondence [ref] .

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.88
In [ref] , $N=3$ Chern-Simons-adjoint theories were discussed.

On Large N Solution of N=3 Chern-Simons-adjoint Theories · Chern-Simons-adjoint theory revisited · 0.95
The worldvolume theory on M2-branes in the flat space-time was constructed in [ref] [ref] [ref] [ref] [ref] whose applicability is, however, limited to the system with two M2-branes.

Selfdual strings and loop space Nahm equations · Introduction · 0.90

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