5,122 research outputs found
Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double
It it known that to get the usual Hamiltonian formulation of lattice
Yang-Mills theory in the temporal gauge one should place on every
link the cotangent bundle of a Lie group. The cotangent bundle may be
considered as a limiting case of a so called Heisenberg double of a Lie group
which is one of the basic objects in the theory of Lie-Poisson and quantum
groups. It is shown in the paper that there is a generalization of the usual
Hamiltonian formulation to the case of the Heisenberg double.Comment: 11 pages, latex, no figure
Stationary strings near a higher-dimensional rotating black hole
We study stationary string configurations in a space-time of a
higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto
equations for a stationary string in the 5D Myers-Perry metric allow a
separation of variables. We present these equations in the first-order form and
study their properties. We prove that the only stationary string configuration
which crosses the infinite red-shift surface and remains regular there is a
principal Killing string. A worldsheet of such a string is generated by a
principal null geodesic and a timelike at infinity Killing vector field. We
obtain principal Killing string solutions in the Myers-Perry metrics with an
arbitrary number of dimensions. It is shown that due to the interaction of a
string with a rotating black hole there is an angular momentum transfer from
the black hole to the string. We calculate the rate of this transfer in a
spacetime with an arbitrary number of dimensions. This effect slows down the
rotation of the black hole. We discuss possible final stationary configurations
of a rotating black hole interacting with a string.Comment: 13 pages, contains additianal material at the end of Section 8, also
small misprints are correcte
Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
We find the Hamiltonian for physical excitations of the classical bosonic
string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained
in a so-called uniform gauge which is related to the static gauge by a 2d
duality transformation. The Hamiltonian is of the Nambu type and depends on two
parameters: a single S^5 angular momentum J and the string tension \lambda. In
the general case both parameters can be finite. The space of string states
consists of short and long strings. In the sector of short strings the large J
expansion with \lambda'=\lambda/J^2 fixed recovers the plane-wave Hamiltonian
and higher-order corrections recently studied in the literature. In the strong
coupling limit \lambda\to \infty, J fixed, the energy of short strings scales
as \sqrt[4]{\lambda} while the energy of long strings scales as \sqrt{\lambda}.
We further show that the gauge-fixed Hamiltonian is integrable by constructing
the corresponding Lax representation. We discuss some general properties of the
monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum
perfectly agrees with the one obtained earlier for some specific cases.Comment: 30 pages, LaTex; v2: a few comments added, misprints corrected,
references adde
A note on gravity-scalar fluctuations in holographic RG flow geometries
We study five-dimensional gravity models with non-vanishing background scalar
fields which are dual to non-conformal boundary field theories. We develop a
procedure to decouple the graviton fluctuations from the scalar ones and apply
it to the simplest case of one scalar field. The quadratic action for the
decoupled scalar fluctuations has a very simple form and can be used to compute
two-point functions. We perform this computation for the two examples of
background RG flow recently considered by DeWolfe and Freedman and find
physically reasonable results.Comment: 13 pages, latex, no figure
Scattering of Straight Cosmic Strings by Black Holes: Weak Field Approximation
The scattering of a straight, infinitely long string moving with velocity
by a black hole is considered. We analyze the weak-field case, where the impact
parameter () is large, and obtain exact solutions to the equations of
motion. As a result of scattering, the string is displaced in the direction
perpendicular to the velocity by an amount , where . The second
term dominates at low velocities . The late-time
solution is represented by a kink and anti-kink, propagating in opposite
directions at the speed of light, and leaving behind them the string in a new
``phase''. The solutions are applied to the problem of string capture, and are
compared to numerical results.Comment: 19 pages, 5 figure
Stringy effect of the holographic correspondence for Dp-brane backgrounds
Based on the holographic conjecture for superstrings on Dp-brane backgrounds
and the dual (p+1)-dimensional gauge theory () given in
hep-th/0308024 and hep-th/0405203, we continue the study of superstring
amplitudes including string higher modes (). We give a prediction to
the two-point functions of operators with large R-charge J. The effect of
stringy modes do not appear as the form of anomalous dimensions except for p=3.
Instead, it gives non-trivial correction to the two-point functions for
supergravity modes. For p=4, the scalar two-point functions for any n behave
like free fields of the effective dimension d_{eff}=6 in the infra-red limit.Comment: 23 pages, typos correcte
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