702 research outputs found

### Tensor Generalizations of Affine Symmetry Vectors

A definition is suggested for affine symmetry tensors, which generalize the
notion of affine vectors in the same way that (conformal) Killing tensors
generalize (conformal) Killing vectors. An identity for these tensors is
proved, which gives the second derivative of the tensor in terms of the
curvature tensor, generalizing a well-known identity for affine vectors.
Additionally, the definition leads to a good definition of homothetic tensors.
The inclusion relations between these types of tensors are exhibited. The
relationship between affine symmetry tensors and solutions to the equation of
geodesic deviation is clarified, again extending known results about Killing
tensors.Comment: 11 page

### Harmonic coordinates in the string and membrane equations

In this note, we first show that the solutions to Cauchy problems for two
versions of relativistic string and membrane equations are diffeomorphic. Then
we investigate the coordinates transformation presented in Ref. [9] (see (2.20)
in Ref. [9]) which plays an important role in the study on the dynamics of the
motion of string in Minkowski space. This kind of transformed coordinates are
harmonic coordinates, and the nonlinear relativistic string equations can be
straightforwardly simplified into linear wave equations under this
transformation

### One-loop Effective Action of the Holographic Antisymmetric Wilson Loop

We systematically study the spectrum of excitations and the one-loop
determinant of holographic Wilson loop operators in antisymmetric
representations of $\mathcal{N}=4$ supersymmetric Yang-Mills theory.
Holographically, these operators are described by D5-branes carrying electric
flux and wrapping an $S^4 \subset S^5$ in the $AdS_5\times S^5$ bulk
background. We derive the dynamics of both bosonic and fermionic excitations
for such D5-branes. A particularly important configuration in this class is the
D5-brane with $AdS_2\times S^4$ worldvolume and $k$ units of electric flux,
which is dual to the circular Wilson loop in the totally antisymmetric
representation of rank $k$. For this Wilson loop, we obtain the spectrum, show
explicitly that it is supersymmetric and calculate the one-loop effective
action using heat kernel techniques.Comment: 42 pages, one tabl

### Helicoidal surfaces with constant anisotropic mean curvature

We study surfaces with constant anisotropic mean curvature which are
invariant under a helicoidal motion. For functionals with axially symmetric
Wulff shapes, we generalize the recently developed twizzler representation of
Perdomo to the anisotropic case and show how all helicoidal constant
anisotropic mean curvature surfaces can be obtained by quadratures

### Classical integrability of chiral $QCD_{2}$ and classical curves

In this letter, classical chiral $QCD_{2}$ is studied in the lightcone gauge
$A_{-}=0$. The once integrated equation of motion for the current is shown to
be of the Lax form, which demonstrates an infinite number of conserved
quantities. Specializing to gauge group SU(2), we show that solutions to the
classical equations of motion can be identified with a very large class of
curves. We demonstrate this correspondence explicitly for two solutions. The
classical fermionic fields associated with these currents are then obtained.Comment: Final version to appear in Mod. Phys. Lett. A. A reference and two
footnotes added. 6 pages revte

### Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems

### The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

The definition of the Einstein 3-form G_a is motivated by means of the
contracted 2nd Bianchi identity. This definition involves at first the complete
curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge
o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior
product. The L_a is equivalent to the Einstein 3-form and represents a certain
contraction of the curvature 2-form. A variational formula of Salgado on
quadratic invariants of the L_a 1-form is discussed, generalized, and put into
proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra

### Vectorial Ribaucour Transformations for the Lame Equations

The vectorial extension of the Ribaucour transformation for the Lame
equations of orthogonal conjugates nets in multidimensions is given. We show
that the composition of two vectorial Ribaucour transformations with
appropriate transformation data is again a vectorial Ribaucour transformation,
from which it follows the permutability of the vectorial Ribaucour
transformations. Finally, as an example we apply the vectorial Ribaucour
transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package

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