# ABJM Wilson loops in the Fermi gas approach

@article{Klemm2012ABJMWL, title={ABJM Wilson loops in the Fermi gas approach}, author={Albrecht Klemm and Marcos Mari{\~n}o and Marc Schiereck and Masoud Soroush}, journal={arXiv: High Energy Physics - Theory}, year={2012} }

The matrix model of ABJM theory can be formulated in terms of a Fermi gas in an external potential. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statistical-mechanical 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…

## 58 Citations

### ABJM Wilson loops in arbitrary representations

- Biology
- 2013

The vacuum expectation values of circular half BPS Wilson loops in arbitrary representations in ABJM theory are found to be reduced to elementary integrations thanks to the Fermi gas formalism and it is shown that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations.

### Instanton corrections of 1/6 BPS Wilson loops in ABJM theory

- Physics
- 2016

A bstractWe study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental…

### Instanton effects in ABJM theory from Fermi gas approach

- Physics
- 2013

A bstractWe study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k = 1, 2, 3, 4,…

### Exact results for Wilson loops in orbifold ABJM theory

- Physics
- 2016

We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d = 3 mathcal = 4 super Chern-Simons-matter theory that could be obtained by orbifolding…

### ABJ fractional brane from ABJM Wilson loop

- Physics
- 2014

A bstractWe present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop…

### Perturbative evaluation of circular 1/2 BPS Wilson loops in $ \mathcal{N}=6 $ super Chern-Simons theories

- Physics
- 2013

A bstractWe present a complete two-loop analysis of the quantum expectation value for circular BPS Wilson loops in ABJ(M) theories. We examine in details the 1/2 BPS case, that requires non-trivial…

### Exact results for ABJ Wilson loops and open-closed duality

- Physics
- 2016

A bstractWe find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the…

### Exact results on the ABJM Fermi gas

- Physics, Mathematics
- 2012

A bstractWe study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the grand partition function of the ABJM theory, and compute exactly the…

### Notes on BPS Wilson Loops and the Cusp Anomalous Dimension in ABJM theory

- Physics
- 2013

We introduce a new purely bosonic, 1 BPS Wilson loop for ABJM theory on S 3 that couples scalar elds to a latitude at an angle on S 2 2 CP 3 . Through localization of this operator, we relate the…

### Instanton bound states in ABJM theory

- Physics
- 2013

A bstractThe partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet…

## References

SHOWING 1-10 OF 61 REFERENCES

### ABJM theory as a Fermi gas

- Physics
- 2012

The partition function on the 3-sphere of many supersymmetric Chern–Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory…

### Exact results for Wilson loops in superconformal Chern-Simons theories with matter

- Physics
- 2010

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model.…

### Exact results in ABJM theory from topological strings

- Physics
- 2010

Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that…

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

- Physics
- 2012

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…

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

- Physics
- 2011

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.…

### A supermatrix model for N = 6 super Chern-Simons-matter theory

- Physics
- 2010

We construct the Wilson loop operator of N = 6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS4…

### An exact prediction of

- Business
- 2000

We propose that the expectation value of a circular BPS-Wilson loop in N=4 supersymmetric Yang--Mills can be calculated exactly, to all orders in a 1/N expansion and to all orders in g{sup 2}N. Using…

### Gravitational corrections in supersymmetric gauge theory and matrix models

- Physics
- 2003

Gravitational corrections in N = 1 and N = 2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides…

### Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

- Physics, Mathematics
- 2010

We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to…

### Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

- Mathematics
- 1994

We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in…