24 research outputs found
Correlation functions of boundary field theory from bulk Green's functions and phases in the boundary theory
In the context of the bulk-boundary correspondence we study the correlation
functions arising on a boundary for different types of boundary conditions. The
most general condition is the mixed one interpolating between the Neumann and
Dirichlet conditions. We obtain the general expressions for the correlators on
a boundary in terms of Green's function in the bulk for the Dirichlet, Neumann
and mixed boundary conditions and establish the relations between the
correlation functions. As an instructive example we explicitly obtain the
boundary correlators corresponding to the mixed condition on a plane boundary
of a domain in flat space . The phases of the boundary theory
with correlators of the Neumann and Dirichlet types are determined. The
boundary correlation functions on sphere are calculated for the Dirichlet
and Neumann conditions in two important cases: when sphere is a boundary of a
domain in flat space and when it is a boundary at infinity of Anti-De
Sitter space . For massless in the bulk theory the Neumann
correlator on the boundary of AdS space is shown to have universal logarithmic
behavior in all AdS spaces. In the massive case it is found to be finite at the
coinciding points. We argue that the Neumann correlator may have a dual
two-dimensional description. The structure of the correlators obtained, their
conformal nature and some recurrent relations are analyzed. We identify the
Dirichlet and Neumann phases living on the boundary of AdS space and discuss
their evolution when the location of the boundary changes from infinity to the
center of the AdS space.Comment: 32 pages, latex, no figure
Two-Dimensional Reduced Theory and General Static Solution for Uncharged Black p-Branes
We derive a two-dimensional effective dilaton - gravity - matter action that
describes the dynamics of an uncharged black p-brane in N dimensions. We show
that this effective theory is completely integrable in the static sector and
establish its general static solution. The solution includes, as a particular
case, the boost symmetric p-brane solution investigated in hep-th/9510202 .Comment: 11 pages, plain LaTex, accepted for publication in Phys. Lett.
Space for Both No-Boundary and Tunneling Quantum States of the Universe
At the minisuperspace level of homogeneous models, the bare probability for a
classical universe has a huge peak at small universes for the Hartle-Hawking
`no-boundary' wavefunction, in contrast to the suppression at small universes
for the `tunneling' wavefunction. If the probability distribution is cut off at
the Planck density (say), this suggests that the former quantum state is
inconsistent with our observations. For inhomogeneous models in which
stochastic inflation can occur, it is known that the idea of including a volume
factor in the observational probability distribution can lead to arbitrarily
large universes' being likely. Here this idea is shown to be sufficient to save
the Hartle-Hawking proposal even at the minisuperspace level (for suitable
inflaton potentials), by giving it enough space to be consistent with
observations.Comment: LaTeX, 20 pages, no figures, blank lines removed, page break inserte
Gauge Invariant Higgs mass bounds from the Physical Effective Potential
We study a simplified version of the Standard Electroweak Model and introduce
the concept of the physical gauge invariant effective potential in terms of
matrix elements of the Hamiltonian in physical states. This procedure allows an
unambiguous identification of the symmetry breaking order parameter and the
resulting effective potential as the energy in a constrained state. We
explicitly compute the physical effective potential at one loop order and
improve it using the RG. This construction allows us to extract a reliable,
gauge invariant bound on the Higgs mass by unambiguously obtaining the scale at
which new physics should emerge to preclude vacuum instability. Comparison is
made with popular gauge fixing procedures and an ``error'' estimate is provided
between the Landau gauge fixed and the gauge invariant results.Comment: 23 pages, 2 figures, REVTE
A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field
We present a solvable model of two-dimensional dilaton-gravity coupled to a
massless scalar field. We locally integrate the field equations and briefly
discuss the properties of the solutions. For a particular choice of the
coupling between the dilaton and the scalar field the model can be interpreted
as the two-dimensional effective theory of 2+1 cylindrical gravity minimally
coupled to a massless scalar field.Comment: 6 pages, RevTeX, to be published in Phys. Rev.
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
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters and of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner.
The classical Hamiltonian written in terms of these variables and their
conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian
operator, and an eigenvalue equation for the ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity are of the form , where
is an integer. It turns out that this result is closely related to
Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure
Effective-Lagrangian approach to precision measurements: the anomalous magnetic moment of the muon
We investigate the use of effective Lagrangians to describe the effects on
high-precision observables of physics beyond the Standard Model. Using the
anomalous magnetic moment of the muon as an example, we detail the use of
effective vertices in loop calculations. We then provide estimates of the
sensitivity of new experiments measuring the muon's to the scale of
physics underlying the Standard Model.Comment: 22 pages, 1 figure, PHYZZX & EPSF, report #s UCRHEP-T98, UM_TH-92-17,
and NSF-ITP-92-122I Revision: The paper will now TeX properly; the content is
unchange
Central charges and boundary fields for two dimensional dilatonic black holes
In this paper we first show that within the Hamiltonian description of
general relativity, the central charge of a near horizon asymptotic symmetry
group is zero, and therefore that the entropy of the system cannot be estimated
using Cardy's formula. This is done by mapping a static black hole to a two
dimensional space. We explain how such a charge can only appear to a static
observer who chooses to stay permanently outside the black hole. Then an
alternative argument is given for the presence of a universal central charge.
Finally we suggest an effective quantum theory on the horizon that is
compatible with the thermodynamics behaviour of the black hole.Comment: 16 pages, no figures, LaTex 2e, references adde
Canonical Quantum Statistics of an Isolated Schwarzschild Black Hole with a Spectrum E_n = sigma sqrt{n} E_P
Many authors - beginning with Bekenstein - have suggested that the energy
levels E_n of a quantized isolated Schwarzschild black hole have the form E_n =
sigma sqrt{n} E_P, n=1,2,..., sigma =O(1), with degeneracies g^n. In the
present paper properties of a system with such a spectrum, considered as a
quantum canonical ensemble, are discussed: Its canonical partition function
Z(g,beta=1/kT), defined as a series for g<1, obeys the 1-dimensional heat
equation. It may be extended to values g>1 by means of an integral
representation which reveals a cut of Z(g,beta) in the complex g-plane from g=1
to infinity. Approaching the cut from above yields a real and an imaginary part
of Z. Very surprisingly, it is the (explicitly known) imaginary part which
gives the expected thermodynamical properties of Schwarzschild black holes:
Identifying the internal energy U with the rest energy Mc^2 requires beta to
have the value (in natural units) beta = 2M(lng/sigma^2)[1+O(1/M^2)], (4pi
sigma^2=lng gives Hawking's beta_H), and yields the entropy S=[lng/(4pi
sigma^2)] A/4 + O(lnA), where A is the area of the horizon.Comment: 14 pages, LaTeX A brief note added which refers to previous work
where the imaginary part of the partition function is related to metastable
states of the syste