1,548 research outputs found
Matrix embeddings on flat and the geometry of membranes
We show that given three hermitian matrices, what one could call a fuzzy
representation of a membrane, there is a well defined procedure to define a set
of oriented Riemann surfaces embedded in using an index function defined
for points in that is constructed from the three matrices and the point.
The set of surfaces is covariant under rotations, dilatations and translation
operations on , it is additive on direct sums and the orientation of the
surfaces is reversed by complex conjugation of the matrices. The index we build
is closely related to the Hanany-Witten effect. We also show that the surfaces
carry information of a line bundle with connection on them.
We discuss applications of these ideas to the study of holographic matrix
models and black hole dynamics.Comment: 41 pages, 3 figures, uses revtex4-1. v2: references added, corrected
an error in attribution of idea
Probing black holes in non-perturbative gauge theory
We use a 0-brane to probe a ten-dimensional near-extremal black hole with N
units of 0-brane charge. We work directly in the dual strongly-coupled quantum
mechanics, using mean-field methods to describe the black hole background
non-perturbatively. We obtain the distribution of W boson masses, and find a
clear separation between light and heavy degrees of freedom. To localize the
probe we introduce a resolving time and integrate out the heavy modes. After a
non-trivial change of coordinates, the effective potential for the probe agrees
with supergravity expectations. We compute the entropy of the probe, and find
that the stretched horizon of the black hole arises dynamically in the quantum
mechanics, as thermal restoration of unbroken U(N+1) gauge symmetry. Our
analysis of the quantum mechanics predicts a correct relation between the
horizon radius and entropy of a black hole.Comment: 30 pages, LaTeX, 8 eps figures. v2: references added. v3: more
reference
Anisotropy beta functions
The flow of couplings under anisotropic scaling of momenta is computed in
theory in 6 dimensions. It is shown that the coupling decreases as
momenta of two of the particles become large, keeping the third momentum fixed,
but at a slower rate than the decrease of the coupling if all three momenta
become large simultaneously. This effect serves as a simple test of effective
theories of high energy scattering, since such theories should reproduce these
deviations from the usual logarithmic scale dependence.Comment: uuencoded ps file, 6 page
Non-minimal coupling and quantum entropy of black hole
Formulating the statistical mechanics for a scalar field with non-minimal
coupling in a black hole background we propose modification of
the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet
condition we suggest some scattering ansatz for the field functions at the
horizon. This modifies the energy spectrum of the system and allows one to
obtain the statistical entropy dependent on the non-minimal coupling. For
the entropy renormalizes the classical Bekenstein-Hawking entropy in
the correct way and agrees with the result previously obtained within the
conical singularity approach. For a positive , however, the results
differ.Comment: 16 pages, latex, no figures; an error in calculation of the entropy
corrected, the entropy now is positive for any non-minimal couplin
Dynamical tachyons on fuzzy spheres
We study the spectrum of off-diagonal fluctuations between displaced fuzzy
spheres in the BMN plane wave matrix model. The displacement is along the plane
of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles
classical tachyons develop and that the spectrum of these modes can be computed
analytically. These tachyons can be related to the familiar Nielsen-Olesen
instabilities in Yang-Mills theory on a constant magnetic background. Many
features of the problem become more apparent when we compare with maximally
supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We
also set up a simple oscillatory trajectory on the displacement between the
fuzzy spheres and study the dynamics of the modes as they become tachyonic for
part of the oscillations. We speculate on their role regarding the possible
thermalization of the system.Comment: 34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added
reference
Remarks on effective action and entanglement entropy of Maxwell field in generic gauge
We analyze the dependence of the effective action and the entanglement
entropy in the Maxwell theory on the gauge fixing parameter in
dimensions. For a generic value of the corresponding vector operator is
nonminimal. The operator can be diagonalized in terms of the transverse and
longitudinal modes. Using this factorization we obtain an expression for the
heat kernel coefficients of the nonminimal operator in terms of the
coefficients of two minimal Beltrami-Laplace operators acting on 0- and
1-forms. This expression agrees with an earlier result by Gilkey et al. Working
in a regularization scheme with the dimensionful UV regulators we introduce
three different regulators: for transverse, longitudinal and ghost modes,
respectively. We then show that the effective action and the entanglement
entropy do not depend on the gauge fixing parameter provided the certain
(-dependent) relations are imposed on the regulators. Comparing the
entanglement entropy with the black hole entropy expressed in terms of the
induced Newton's constant we conclude that their difference, the so-called
Kabat's contact term, does not depend on the gauge fixing parameter . We
consider this as an indication of gauge invariance of the contact term.Comment: 15 pages; v2: typos in eqs. (31), (32), (34), (36) corrected;
discussion in section 6 expande
Local bulk operators in AdS/CFT: a boundary view of horizons and locality
We develop the representation of local bulk fields in AdS by non-local
operators on the boundary, working in the semiclassical limit and using AdS_2
as our main example. In global coordinates we show that the boundary operator
has support only at points which are spacelike separated from the bulk point.
We construct boundary operators that represent local bulk operators inserted
behind the horizon of the Poincare patch and inside the Rindler horizon of a
two dimensional black hole. We show that these operators respect bulk locality
and comment on the generalization of our construction to higher dimensional AdS
black holes.Comment: 28 pages, 4 figures, late
Edges and Diffractive Effects in Casimir Energies
The prototypical Casimir effect arises when a scalar field is confined
between parallel Dirichlet boundaries. We study corrections to this when the
boundaries themselves have apertures and edges. We consider several geometries:
a single plate with a slit in it, perpendicular plates separated by a gap, and
two parallel plates, one of which has a long slit of large width, related to
the case of one plate being semi-infinite. We develop a general formalism for
studying such problems, based on the wavefunctional for the field in the gap
between the plates. This formalism leads to a lower dimensional theory defined
on the open regions of the plates or boundaries. The Casimir energy is then
given in terms of the determinant of the nonlocal differential operator which
defines the lower dimensional theory. We develop perturbative methods for
computing these determinants. Our results are in good agreement with known
results based on Monte Carlo simulations. The method is well suited to
isolating the diffractive contributions to the Casimir energy.Comment: 32 pages, LaTeX, 9 figures. v2: additional discussion of
renormalization procedure, version to appear in PRD. v3: corrected a sign
error in (70
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