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 On a gravity dual to flavored topological quantum mechanics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrey Feldman
Keyword(s):  
Quantum Mechanics ◽  
Effective Field ◽  
Abjm Theory ◽  
Yang Mills ◽  
Topological Quantum ◽  
Higher Derivatives ◽  
Structure Constants ◽  
Holographic Description ◽  
M Theory ◽  
Chern Simons

Abstract In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $$ \mathcal{N} $$ N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

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 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 Notes on hyperloops in $$ \mathcal{N} $$ = 4 Chern-Simons-matter theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nadav Drukker ◽  
Marcia Tenser ◽  
Diego Trancanelli
Keyword(s):  
Moduli Spaces ◽  
Three Dimensional ◽  
Discrete Data ◽  
Parameter Family ◽  
Wilson Loops ◽  
Matter Theory ◽  
M Theory ◽  
Chern Simons ◽  
Two Parameter ◽  
Matter Fields

Abstract We present new circular Wilson loops in three-dimensional $$ \mathcal{N} $$ N = 4 quiver Chern-Simons-matter theory on S3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.

scholarly journals The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Damon J. Binder ◽  
Shai M. Chester ◽  
Max Jerdee ◽  
Silviu S. Pufu
Keyword(s):  
Block Decomposition ◽  
Point Function ◽  
Present Evidence ◽  
Bootstrap Techniques ◽  
Wide Range ◽  
Higher Spin ◽  
Tensor Multiplet ◽  
Higher Spins ◽  
M Theory ◽  
Chern Simons

Abstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

scholarly journals A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Grand Unification ◽  
De Sitter ◽  
Sitter Group ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
M Theory ◽  
Chern Simons ◽  
Topological Part ◽  
Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

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