scholarly journals Triality and the consistent reductions on AdS3 × S3

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Camille Eloy ◽  
Gabriel Larios ◽  
Henning Samtleben
Keyword(s):  
Field Theory ◽  
Nonlinear Dynamics ◽  
Parameter Space ◽  
Three Dimensional ◽  
Parameter Family ◽  
Duality Group ◽  
Consistent Truncations ◽  
Two Parameter ◽  
Kaluza Klein

Abstract We study compactifications on AdS3×S3 and deformations thereof. We exploit the triality symmetry of the underlying duality group SO(4,4) of three-dimensional supergravity in order to construct and relate new consistent truncations. For non-chiral D = 6, $$ \mathcal{N} $$ N 6d = (1, 1) supergravity, we find two different consistent truncations to three-dimensional supergravity, retaining different subsets of Kaluza-Klein modes, thereby offering access to different subsectors of the full nonlinear dynamics. As an application, we construct a two-parameter family of AdS3 × M3 backgrounds on squashed spheres preserving U(1)2 isometries. For generic value of the parameters, these solutions break all supersymmetries, yet they remain perturbatively stable within a non-vanishing region in parameter space. They also contain a one-parameter family of $$ \mathcal{N} $$ N = (0, 4) supersymmetric AdS3 × M3 backgrounds on squashed spheres with U(2) isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.

scholarly journals The spectrum of marginally-deformed $$ \mathcal{N} $$ = 2 CFTs with AdS4 S-fold duals of type IIB

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Mattia Cesàro ◽  
Gabriel Larios ◽  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Yang Mills ◽  
Conformal Field ◽  
Operator Spectrum ◽  
Two Parameter ◽  
Kaluza Klein

Abstract A holographic duality was recently established between an $$ \mathcal{N} $$ N = 4 non-geometric AdS4 solution of type IIB supergravity in the so-called S-fold class, and a three- dimensional conformal field theory (CFT) defined as a limit of $$ \mathcal{N} $$ N = 4 super-Yang-Mills at an interface. Using gauged supergravity, the $$ \mathcal{N} $$ N = 2 conformal manifold (CM) of this CFT has been assessed to be two-dimensional. Here, we holographically characterise the large-N operator spectrum of the marginally-deformed CFT. We do this by, firstly, providing the algebraic structure of the complete Kaluza-Klein (KK) spectrum on the associated two-parameter family of AdS4 solutions. And, secondly, by computing the $$ \mathcal{N} $$ N = 2 super-multiplet dimensions at the first few KK levels on a lattice in the CM, using new exceptional field theory techniques. Our KK analysis also allows us to establish that, at least at large N, this $$ \mathcal{N} $$ N = 2 CM is topologically a non-compact cylindrical Riemann surface bounded on only one side.

PHASE HOLONOMY OF THE VACUUM IN THREE-DIMENSIONAL GAUGE THEORIES

1992 ◽  
Vol 07 (20) ◽  
pp. 4937-4948
Author(s):  
ROBERT LINK
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Theories ◽  
Magnetic Monopole ◽  
Three Dimensional ◽  
Parameter Family ◽  
Two Parameter ◽  
Dirac Hamiltonian

The phase two-form of Berry in the neighborhood of a degeneracy of the Fock vacuum of a semisimple, nonabelian, second-quantized, relativistic fermion-background gauge field Hamiltonian is shown to be that of the Dirac magnetic monopole—thus extending a result of Berry to field theory. The Dirac Hamiltonian for an SU(2) fermion on the two-sphere is solved in a particular two-parameter family of background instanton gauge potentials as an explicit illustrative example.

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 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.

A Nonlinear Dynamics Analysis of Vortex-Structure Interaction Models

2001 ◽  
Vol 123 (4) ◽  
pp. 475-479 ◽  
Author(s):  
N. W. Mureithi ◽  
S. Goda ◽  
H. Kanki ◽  
T. Nakamura
Keyword(s):  
Nonlinear Dynamics ◽  
Parameter Space ◽  
Vortex Structure ◽  
Three Dimensional ◽  
Order Model ◽  
Third Order ◽  
Interaction Models ◽  
Structure Interaction ◽  
Lock In ◽  
Fifth Order

Vortex-structure interaction models are studied in the work presented here. The third- order model by Hartlen and Currie (HC model) can reproduce the correct response amplitude, while a fifth-order model by Landl predicts the observed hysterisis effect. Using concepts from nonlinear dynamics and bifurcation theory, the range of possible dynamics of the models is investigated in parameter space; essentially, a class of nonlinear oscillators deriving “naturally” from the HC model is studied. It is found that perturbations of the HC model in parameter space lead to qualitatively physically meaningful dynamics. Forced excitation of the HC model is the highlight of the work. In this case, it is shown that a subharmonic lock-in predicted by the model may be related to a three-dimensional secondary subharmonic instability of a periodic flow. Experimental results are presented for comparison.

Instantaneous Kinematics of a Tangent-Plane in Two-Parameter Space Motion

1994 ◽  
Vol 116 (1) ◽  
pp. 210-214
Author(s):  
D. P. Sathyadev ◽  
A. H. Soni
Keyword(s):  
Parameter Space ◽  
Tangent Plane ◽  
Plane Motion ◽  
Parameter Family ◽  
Spherical Image ◽  
Space Motion ◽  
Two Parameter

A tangent-plane undergoing two-parameter motion envelopes a surface called the tangent-plane envelope. Such surfaces can be considered as the envelope of a two-parameter family of planes or ∞2 family of planes. The properties of the tangent-plane motion are characterized through the properties of the spherical image of the normal to the surface it envelopes. This paper presents a methodology to locate a family of planes that envelope surfaces with similar characteristics.

Singularities of line congruences

2003 ◽  
Vol 133 (6) ◽  
pp. 1341-1359 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Kentaro Saji ◽  
Nobuko Takeuchi
Keyword(s):  
Three Dimensional ◽  
Parameter Family ◽  
General Line ◽  
Line Congruence ◽  
Lagrangian Singularities ◽  
Generic Singularities ◽  
Two Parameter

A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

scholarly journals Super-Chern-Simons spectra from exceptional field theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Oscar Varela
Keyword(s):  
Field Theory ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Field Theories ◽  
Specific Class ◽  
Chern Simons ◽  
Kaluza Klein

Abstract Exceptional Field Theory has been recently shown to be very powerful to compute Kaluza-Klein spectra. Using these techniques, the mass matrix of Kaluza-Klein vector perturbations about a specific class of AdS4 solutions of D = 11 and massive type IIA supergravity is determined. These results are then employed to characterise the complete supersymmetric spectrum about some notable $$ \mathcal{N} $$ N = 2 and $$ \mathcal{N} $$ N = 3 AdS4 solutions in this class, which are dual to specific three-dimensional superconformal Chern-Simons field theories.

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.

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