64 research outputs found
Quantum corrections to the noncommutative kink
We calculate quantum corrections to the mass of noncommutative phi^4 kink in
(1+1) dimensions for intermediate and large values of the noncommutativity
parameter theta. All one-loop divergences are removed by a mass renormalization
(which is different from the one required in the topologically trivial sector).
For large theta quantum corrections to the mass grow linearly with theta
signaling about possible break down of the perturbative expansion.Comment: 18 pages, v2: minor change
Quantum aspects of a noncommutative supersymmetric kink
We consider quantum corrections to a kink of noncommutative supersymmetric
phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of
time derivatives in the action, we are able to define supercharges and a
Hamiltonian by using an unconventional canonical formalism. We calculate the
quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of
fluctuations) which coincides with its' value in corresponding commutative
theory independently of the noncommutativity parameter. The renormalization
also proceeds precisely as in the commutative case. The vacuum expectation
value of the new Hamiltonian is also calculated and appears to be consistent
with the value of the quantum energy E of the kink.Comment: 20 pages, v2: a reference adde
Thorny Spheres and Black Holes with Strings
We consider thorny spheres, that is 2-dimensional compact surfaces which are
everywhere locally isometric to a round sphere except for a finite number
of isolated points where they have conical singularities. We use thorny spheres
to generate, from a spherically symmetric solution of the Einstein equations,
new solutions which describe spacetimes pierced by an arbitrary number of
infinitely thin cosmic strings radially directed. Each string produces an angle
deficit proportional to its tension, while the metric outside the strings is a
locally spherically symmetric solution. We prove that there can be arbitrary
configurations of strings provided that the directions of the strings obey a
certain equilibrium condition. In general this equilibrium condition can be
written as a force-balance equation for string forces defined in a flat 3-space
in which the thorny sphere is isometrically embedded, or as a constraint on the
product of holonomies around strings in an alternative 3-space that is flat
except for the strings. In the case of small string tensions, the constraint
equation has the form of a linear relation between unit vectors directed along
the string axes.Comment: 37 pages, 11 figure
New inequality for Wilson loops from AdS/CFT
The strong subadditivity is the most important inequality which entanglement
entropy satisfies. Based on the AdS/CFT conjecture, entanglement entropy in CFT
is equal to the area of the minimal surface in AdS space. It is known that a
Wilson loop can also be holographically computed from the minimal surface in
AdS space. In this paper, we argue that Wilson loops also satisfy a similar
inequality, and find several evidences of it.Comment: 16 pages (removed unnecessary figures
Two-dimensional Quantum-Corrected Eternal Black Hole
The one-loop quantum corrections to geometry and thermodynamics of black hole
are studied for the two-dimensional RST model. We chose boundary conditions
corresponding to the eternal black hole being in the thermal equilibrium with
the Hawking radiation. The equations of motion are exactly integrated. The one
of the solutions obtained is the constant curvature space-time with dilaton
being a constant function. Such a solution is absent in the classical theory.
On the other hand, we derive the quantum-corrected metric (\ref{solution})
written in the Schwarzschild like form which is a deformation of the classical
black hole solution \cite{5d}. The space-time singularity occurs to be milder
than in classics and the solution admits two asymptotically flat black hole
space-times lying at "different sides" of the singularity. The thermodynamics
of the classical black hole and its quantum counterpart is formulated. The
thermodynamical quantities (energy, temperature, entropy) are calculated and
occur to be the same for both the classical and quantum-corrected black holes.
So, no quantum corrections to thermodynamics are observed. The possible
relevance of the results obtained to the four-dimensional case is discussed.Comment: Latex, 28 pges; minor corrections in text and abstract made and new
references adde
Kaluza-Klein Method in Theory of Rotating Quantum Fields
Quantum fields on a stationary space-time in a rotating Killing reference
frame are considered. Finding solutions of wave equations in this frame is
reduced to a fiducial problem on a static background. The rotation results in a
gauge connection in a way similar to appearance of gauge fields in Kaluza-Klein
models. Such a Kaluza-Klein method in theory of rotating quantum fields enables
one to simplify computations and get a number of new results similar to those
established for static backgrounds. In particular, we find with its help
functional form of free energy at high temperatures. Applications of these
results to quantum fields near rotating black holes are briefly discussed.Comment: 23 pages, late
A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field always can be expressed as the spatial
integral of , where are the constraints
associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late
Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
Logarithmic corrections to the extremal black hole entropy can be computed
purely in terms of the low energy data -- the spectrum of massless fields and
their interaction. The demand of reproducing these corrections provides a
strong constraint on any microscopic theory of quantum gravity that attempts to
explain the black hole entropy. Using quantum entropy function formalism we
compute logarithmic corrections to the entropy of half BPS black holes in N=2
supersymmetric string theories. Our results allow us to test various proposals
for the measure in the OSV formula, and we find agreement with the measure
proposed by Denef and Moore if we assume their result to be valid at weak
topological string coupling. Our analysis also gives the logarithmic
corrections to the entropy of extremal Reissner-Nordstrom black holes in
ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page
Entanglement entropy of two dimensional systems and holography
In this note a new method for computing the entanglement entropy of a CFT
holographically is explored. It consists of finding a bulk background with a
boundary metric that has the conical singularities needed to compute the
entanglement entropy in the usual QFT definition. An explicit calculation is
presented for d=2.Comment: 20 pages, 1 figure: v2 typos fixed, references and comments adde
AdS/CFT and Strong Subadditivity of Entanglement Entropy
Recently, a holographic computation of the entanglement entropy in conformal
field theories has been proposed via the AdS/CFT correspondence. One of the
most important properties of the entanglement entropy is known as the strong
subadditivity. This requires that the entanglement entropy should be a concave
function with respect to geometric parameters. It is a non-trivial check on the
proposal to see if this property is indeed satisfied by the entropy computed
holographically. In this paper we examine several examples which are defined by
annuli or cusps, and confirm the strong subadditivity via direct calculations.
Furthermore, we conjecture that Wilson loop correlators in strongly coupled
gauge theories satisfy the same relation. We also discuss the relation between
the holographic entanglement entropy and the Bousso bound.Comment: 29 pages, harvmac, 7 figures, references adde
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