scholarly journals SUPERSYMMETRIC WILSON LOOPS WITH GENERAL CONTOURS IN ABJM THEORY

2013 ◽  
Vol 28 (33) ◽  
pp. 1350150 ◽  
Author(s):  
NAKWOO KIM
Keyword(s):  
Scalar Field ◽  
Wilson Loops ◽  
Abjm Theory ◽  
Expectation Value ◽  
Field Coupling ◽  
Matter Theory ◽  
Chern Simons

We consider general supersymmetric Wilson loops in ABJM model, which is Chern–Simons-matter theory in (2+1) dimensions with 𝒩 = 6 supersymmetry. The Wilson loops of our interest are so-called Zarembo-type: they have generic contours in spacetime, but the scalar field coupling is arranged accordingly so that there are unbroken supersymmetries. Following the supermatrix construction of Wilson loops by Drukker and Trancanelli and the generalization by Griguolo et al., we study 1/6-BPS Wilson loops and check that their expectation value is protected using perturbation up to two loops. We also study the dual string configuration in AdS4×ℂℙ3 background and check the supersymmetry.

scholarly journals M2-BRANES AND AdS/CFT

2010 ◽  
Vol 25 (02n03) ◽  
pp. 332-350 ◽  
Author(s):  
IGOR R. KLEBANOV
Keyword(s):  
Abjm Theory ◽  
Dual Formulation ◽  
Matter Theory ◽  
Monopole Operators ◽  
M Theory ◽  
Chern Simons

We provide a brief introduction to the ABJM theory, the level kU(N) × U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2 -branes. We discuss its dual formulation in terms of M -theory on AdS4 × S7/ℤk and review some of the evidence in favor of the conjecture. We end with a brief discussion of the important role played by the monopole operators.

scholarly journals NONPLANAR INTEGRABILITY AND PARITY IN ABJ THEORY

2013 ◽  
Vol 28 (12) ◽  
pp. 1350043 ◽  
Author(s):  
BADR AWAD ELSEID MOHAMMED
Keyword(s):  
String Theory ◽  
Harmonic Oscillators ◽  
Schur Polynomials ◽  
Gauge Invariant ◽  
Abjm Theory ◽  
Anomalous Dimensions ◽  
Matter Theory ◽  
Dilatation Operator ◽  
Chern Simons ◽  
Double Limit

In this paper, we study the action of the nonplanar two-loop dilatation operator in an SU(2)×SU(2) subsector of the ABJ Chern–Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the nonplanar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.

scholarly journals NUMERICAL STUDIES OF THE ABJM THEORY FOR ARBITRARY N AT ARBITRARY COUPLING CONSTANT

2013 ◽  
Vol 21 ◽  
pp. 203-205
Author(s):  
MASAZUMI HONDA ◽  
MASANORI HANADA ◽  
YOSHINORI HONMA ◽  
JUN NISHIMURA ◽  
SHOTARO SHIBA ◽  
...  
Keyword(s):  
Fermi Gas ◽  
Coupling Constant ◽  
Abjm Theory ◽  
Localization Method ◽  
Arbitrary Coupling ◽  
Numerical Studies ◽  
Matter Theory ◽  
The Matrix ◽  
Genus Expansion ◽  
Chern Simons

We show that the ABJM theory, which is an [Formula: see text] superconformal U (N) × U (N) Chern-Simons matter theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model derived by using the localization method. Here we calculate the free energy, and show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion.

scholarly journals 3d $$ \mathcal{N} $$ = 2 Chern-Simons-matter theory, Bethe ansatz, and quantum K -theory of Grassmannians

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Kazushi Ueda ◽  
Yutaka Yoshida
Keyword(s):  
Bethe Ansatz ◽  
Correlation Functions ◽  
Quantum Cohomology ◽  
Frobenius Algebra ◽  
Wilson Loops ◽  
Small Quantum ◽  
Starting Point ◽  
Matter Theory ◽  
Verlinde Algebras ◽  
Chern Simons

Abstract We study a correspondence between 3d $$ \mathcal{N} $$ N = 2 topologically twisted Chern-Simons-matter theories on S1× Σg and quantum K -theory of Grassmannians. Our starting point is a Frobenius algebra depending on a parameter β associated with an algebraic Bethe ansatz introduced by Gorbounov-Korff. They showed that the Frobenius algebra with β = −1 is isomorphic to the (equivariant) small quantum K -ring of the Grassmannian, and the Frobenius algebra with β = 0 is isomorphic to the equivariant small quantum cohomology of the Grassmannian. We apply supersymmetric localization formulas to the correlation functions of supersymmetric Wilson loops in the Chern-Simons-matter theory and show that the algebra of Wilson loops is isomorphic to the Frobenius algebra with β = −1. This allows us to identify the algebra of Wilson loops with the quantum K - ring of the Grassmannian. We also show that correlation functions of Wilson loops on S1× Σg satisfy the axiom of 2d TQFT. For β = 0, we show the correspondence between an A-twisted GLSM, the Frobenius algebra for β = 0, and the quantum cohomology of the Grassmannian. We also discuss deformations of Verlinde algebras, omega-deformations, and the K -theoretic I -functions of Grassmannians with level structures.

scholarly journals Supersymmetric Wilson loops in super-Chern–Simons-matter theory

2010 ◽  
Vol 825 (1-2) ◽  
pp. 38-51 ◽  
Author(s):  
Bin Chen ◽  
Jun-Bao Wu
Keyword(s):  
Wilson Loops ◽  
Matter Theory ◽  
Chern Simons

scholarly journals Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory

2010 ◽  
Vol 2010 (8) ◽  
Author(s):  
Johannes M. Henn ◽  
Jan Plefka ◽  
Konstantin Wiegandt
Keyword(s):  
Wilson Loops ◽  
Abjm Theory ◽  
Chern Simons

AN INTERPRETATION OF THE ABELIAN CHERN-SIMONS VACUUM HOLONOMY

1990 ◽  
Vol 05 (03) ◽  
pp. 559-569 ◽  
Author(s):  
GUILLERMO ZEMBA
Keyword(s):  
Physical Model ◽  
Three Dimensional ◽  
Physical Significance ◽  
Constant Time ◽  
Simons Theory ◽  
Wilson Loops ◽  
Expectation Value ◽  
Points Of View ◽  
Chern Simons ◽  
Chern Simons Theory

It is shown that the recently discovered vacuum holonomy in the pure Abelian Chern-Simons theory in 2+1 dimensions can be interpreted as the expectation value of the holonomy operator of Wilson loops once the theory is defined on a constant time plane. This may be accomplished by a prescription that connects the two- and three-dimensional points of view. The projected holonomy is framing-dependent and coincides with the previous result if a canonical framing is used. A physical model is considered to discuss its physical significance.

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