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 holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

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 Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

scholarly journals F-THEORY FLUXES, CHIRALITY AND CHERN-SIMONS THEORIES

2013 ◽  
Vol 21 ◽  
pp. 200-202
Author(s):  
HIROTAKA HAYASHI
Keyword(s):  
Three Dimensional ◽  
M Theory ◽  
Chern Simons

We have established a relation between the four-dimensional chiral index in F-theory compactifications and the three-dimensional Chern-Simons coupling in M-theory compactifications by using F-theory - M-theory duality. The content of this article is based on our recent paper,1 which is in collaboration with Thomas W. Grimm.

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 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 ARE THERE ANY NEW VACUA OF GAUGED ${\mathcal N}=8$ SUPERGRAVITY IN FOUR DIMENSIONS?

2010 ◽  
Vol 25 (09) ◽  
pp. 1819-1851 ◽  
Author(s):  
CHANGHYUN AHN ◽  
KYUNGSUNG WOO
Keyword(s):  
Domain Wall ◽  
Cosmological Constant ◽  
Critical Point ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Four Dimensions ◽  
Matter Theory ◽  
Chern Simons ◽  
Constraint Surface

We consider the most general SU(3) singlet space of gauged [Formula: see text] supergravity in four dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we eventually obtain the new scalar potential. For the two extreme limits, we reproduce the previous results found by Warner in 1983. In particular, for the [Formula: see text] critical point, we find the constraint surface parametrized by three scalar fields on which the cosmological constant has the same value. We obtain the BPS domain-wall solutions for restricted scalar submanifold. We also describe the three-dimensional mass-deformed superconformal Chern–Simons matter theory dual to the above supersymmetric flows in four dimensions.

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