scholarly journals Warped AdS2 and SU(1, 1|4) symmetry in Type IIB

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
David Corbino
Keyword(s):  
Riemann Surface ◽  
Trivial Solution ◽  
Existence Of Solutions ◽  
Lie Superalgebra ◽  
Two Dimensional ◽  
Supersymmetric Solution ◽  
Horizon Limit

Abstract We investigate the existence of solutions with 16 supersymmetries to Type IIB supergravity on a spacetime of the form AdS2× S5× S1 warped over a two-dimensional Riemann surface Σ. The existence of the Lie superalgebra SU(1, 1|4) ⊂ PSU(2, 2|4), whose maximal bosonic subalgebra is SO(1, 2)⊕SO(6)⊕SO(2), motivates the search for half-BPS solutions with this isometry that are asymptotic to AdS5×S5. We reduce the BPS equations to the Ansatz for the bosonic fields and supersymmetry generators compatible with these symmetries, then show that the only non-trivial solution is the maximally supersymmetric solution AdS5× S5. We argue that this implies that no solutions exist for fully back-reacted D7 probe or D7/D3 intersecting branes whose near-horizon limit is of the form AdS2× S5× S1× Σ.

Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

On uniqueness and solvability in the linearized two-dimensional problem of a supercritical stream about a surface-piercing body

1995 ◽  
Vol 450 (1939) ◽  
pp. 233-253 ◽  
Keyword(s):  
Free Surface ◽  
Linear Relation ◽  
Existence Of Solutions ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Free Surface Elevation ◽  
Unique Existence ◽  
Velocity Circulation ◽  
Well Posed

Uniqueness and solvability theorems are proved for a well-posed formulation of the two-dimensional Neumann-Kelvin problem (the modified Neumann-Kelvin problem) in the case, when a body is partly immersed in a supercritical stream. Uniqueness is provided by two supplementary conditions which prescribe (i) additional flux at infinity downstream due to presence of body and (ii) a linear relation between the free-surface elevation at stern point and the velocity circulation along wetted contour. Two versions of source method are developed to find a solution. The first version is simpler, but it fails for some irregular values of the body’s velocity. In the second ver­sion complex sources’ strengths are used, avoiding irregular values and establishing the unique existence of solutions.

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

Positive Solutions of the Falkner–Skan Equation Arising in the Boundary Layer Theory

2008 ◽  
Vol 51 (3) ◽  
pp. 386-398 ◽  
Author(s):  
K. Q. Lan ◽  
G. C. Yang
Keyword(s):  
Boundary Layer ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Viscous Incompressible Fluid ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
New Techniques ◽  
Numerical Result ◽  
Two Dimensional Flow ◽  
Equivalence Result

AbstractThe well-known Falkner–Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to λπ/2, where λ ∈ ℝ is a parameter involved in the equation. It is known that there exists λ* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each λ ≥ λ* and has no positive solutions for λ < λ*. The known numerical result shows λ* = –0.1988. In this paper, λ* ∈ [–0.4,–0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner–Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner–Skan equation.

scholarly journals BRST COHOMOLOGY IN BELTRAMI PARAMETRIZATION

1996 ◽  
Vol 11 (02) ◽  
pp. 375-393 ◽  
Author(s):  
LIVIU TĂTARU ◽  
ION V. VANCEA
Keyword(s):  
Field Theory ◽  
Riemann Surface ◽  
Complex Structure ◽  
Theory Model ◽  
Two Dimensional ◽  
Field Theory Model ◽  
Scalar Matter ◽  
Brst Cohomology ◽  
Lagrangian Field Theory ◽  
Matter Fields

We study the BRST cohomology within a local conformal Lagrangian field theory model built on a two-dimensional Riemann surface with no boundary. We deal with the case of the complex structure parametrized by the Beltrami differential and the scalar matter fields. The computation of all elements of the BRST cohomology is given.

A FAMILY OF SURFACES CONSTRUCTED FROM GENUS 2 CURVES

2007 ◽  
Vol 18 (05) ◽  
pp. 585-612 ◽  
Author(s):  
CHAD SCHOEN
Keyword(s):  
Riemann Surface ◽  
Two Dimensional ◽  
Hodge Conjecture ◽  
Analytic Variety ◽  
Genus 2 ◽  
Complex Analytic Variety ◽  
Projective Manifolds ◽  
Genus 2 Curves ◽  
Complex Projective

We consider the deformations of the two-dimensional complex analytic variety constructed from a genus 2 Riemann surface by attaching its self-product to its Jacobian in an elementary way. The deformations are shown to be unobstructed, the variety smooths to give complex projective manifolds whose invariants are computed and whose images under Albanese maps (re)verify an instance of the Hodge conjecture for certain abelian fourfolds.

FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND ON A SPHERE

2007 ◽  
Vol 22 (21) ◽  
pp. 3643-3653 ◽  
Author(s):  
YU-XIAO LIU ◽  
LI ZHAO ◽  
LI-JIE ZHANG ◽  
YI-SHI DUAN
Keyword(s):  
Riemann Surface ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Topological Structure ◽  
The Self ◽  
Two Dimensional ◽  
Zero Modes ◽  
Self Duality ◽  
Effective Lagrangian ◽  
Topological Term

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra sphere and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a sphere in two simple cases are obtained.

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