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 NONPLANAR INTEGRABILITY: BEYOND THE SU(2) SECTOR

2011 ◽  
Vol 26 (26) ◽  
pp. 4553-4583 ◽  
Author(s):  
ROBERT DE MELLO KOCH ◽  
BADR AWAD ELSEID MOHAMMED ◽  
STEPHANIE SMITH
Keyword(s):  
Harmonic Oscillators ◽  
Projection Operators ◽  
Young Diagrams ◽  
Schur Polynomials ◽  
Recursion Relations ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Analytic Expressions ◽  
The One ◽  
Kravchuk Polynomials

We compute the one-loop anomalous dimensions of restricted Schur polynomials with a classical dimension Δ~O(N). The operators that we consider are labeled by Young diagrams with two long columns or two long rows. Simple analytic expressions for the action of the dilatation operator are found. The projection operators needed to define the restricted Schur polynomials are constructed by translating the problem into a spin chain language, generalizing earlier results obtained in the SU(2) sector of the theory. The diagonalization of the dilatation operator reduces to solving five term recursion relations. The recursion relations can be solved exactly in terms of products of symmetric Kravchuk polynomials with Hahn polynomials. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable, extending a similar conclusion reached for the SU(2) sector of the theory.

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 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 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 DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

scholarly journals REMARKS ON A CHERN–SIMONS-LIKE COUPLING

2011 ◽  
Vol 26 (37) ◽  
pp. 2813-2821
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Static Potential ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Hidden Sector ◽  
Dependent Variables ◽  
Qualitative Nature ◽  
Path Dependent ◽  
Chern Simons

We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar U (1) QED photon via a Chern–Simons-like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar U (1) QED photon and a second massive gauge field living in the so-called U (1)h hidden-sector, inside a superconducting box.

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