68 research outputs found
The volume of the moduli space of flat connections on a nonorientable 2-manifold
We compute the Riemannian volume on the moduli space of flat connections on a
nonorientable 2-manifold, for a natural class of metrics. We also show that
Witten's volume formula for these moduli spaces may be derived using Haar
measure, and we give a new proof of Witten's volume formula for the moduli
space of flat connections on an orientable surface using Haar measure.Comment: 31 pages, LaTeX, manuscript substantially revised. To appear in
Communications in Mathematical Physic
Is There Really a de Sitter/CFT Duality
In this paper a de Sitter Space version of Black Hole Complementarity is
formulated which states that an observer in de Sitter Space describes the
surrounding space as a sealed finite temperature cavity bounded by a horizon
which allows no loss of information. We then discuss the implications of this
for the existence of boundary correlators in the hypothesized dS/cft
correspondence. We find that dS complementarity precludes the existence of the
appropriate limits. We find that the limits exist only in approximations in
which the entropy of the de Sitter Space is infinite. The reason that the
correlators exist in quantum field theory in the de Sitter Space background is
traced to the fact that horizon entropy is infinite in QFT.Comment: 12 Figures, STIAS Workshop on Quantum Gravit
Holomorphic Anomalies and the Nonrenormalization Theorem
It has been argued that the superpotential can be renormalized in the
presence of massless particles. Possible implications which have been
considered include the restoration of supersymmetry at higher loops or a shift
to a supersymmetric vacuum state. We argue that even in the presence of
massless particles, there are no new contributions to the superpotential at any
order in perturbation theory. This confirms the utility of the Wilsonian
superpotential for analyzing the moduli space of the low energy theory.Comment: 9 pages, LaTeX, 1 .ps figure, psfig.sty include
A Large Mass Hierarchy from a Small Extra Dimension
We propose a new higher-dimensional mechanism for solving the Hierarchy
Problem. The Weak scale is generated from a large scale of order the Planck
scale through an exponential hierarchy. However, this exponential arises not
from gauge interactions but from the background metric (which is a slice of
AdS_5 spacetime). This mechanism relies on the existence of only a single
additional dimension. We demonstrate a simple explicit example of this
mechanism with two three-branes, one of which contains the Standard Model
fields. The experimental consequences of this scenario are new and dramatic.
There are fundamental spin-2 excitations with mass of weak scale order, which
are coupled with weak scale as opposed to gravitational strength to the
standard model particles. The phenomenology of these models is quite distinct
from that of large extra dimension scenarios; none of the current constraints
on theories with very large extra dimensions apply.Comment: 9 pages, LaTe
Entropy-Area Relations in Field Theory
We consider the contribution to the entropy from fields in the background of
a curved time-independent metric. To account for the curvature of space, we
postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy
naturally implies an IR cutoff on distance. With this procedure, we calculate
the scalar contribution in a background anti-de Sitter space, the exterior of a
black hole, and de Sitter space. In all cases, we find results that can be
simply interpreted in terms of local energy and proper volume, yielding insight
into the apparent reduced dimensionality of systems with gravity.Comment: 20 pages, 1 figur
Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds
We consider the most general three-state spin chain with U(1)^3 symmetry and
nearest neighbour interaction. Our model contains as a special case the spin
chain describing the holomorphic three scalar sector of the three parameter
complex deformation of N=4 SYM, dual to type IIB string theory in the
generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the
coordinate space Bethe ansatz, calculate the S-matrix and determine for which
choices of parameters the S-matrix fulfills the Yang-Baxter equations. For
these choices of parameters we furthermore write down the R-matrix. We find in
total four classes of integrable models. In particular, each already known
model of the above type is nothing but one in a family of such models.Comment: 16 pages, 3 figures, references correcte
Comment on nonperturbative effects in
Uncertainties in the theoretical prediction for the inclusive decay rate are discussed. We emphasize that there is no operator
product expansion for this process. Nonetheless, some nonperturbative effects
involving a virtual loop are calculable using the operator product
expansion. They give a contribution to the decay rate that involves the B meson
matrix element of an infinite tower of operators. The higher dimension
operators give effects that are only suppressed by powers of
, but come with small coefficients.Comment: 9 pages revtex, 2 figures included; minor changes, to appear in Phys.
Lett.
Out Of This World Supersymmetry Breaking
We show that in a general hidden sector model, supersymmetry breaking
necessarily generates at one-loop a scalar and gaugino mass as a consequence of
the super-Weyl anomaly. We study a scenario in which this contribution
dominates. We consider the Standard Model particles to be localized on a
(3+1)-dimensional subspace or ``3-brane'' of a higher dimensional spacetime,
while supersymmetry breaking occurs off the 3-brane, either in the bulk or on
another 3-brane. At least one extra dimension is assumed to be compactified
roughly one to two orders of magnitude below the four-dimensional Planck scale.
This framework is phenomenologically very attractive; it introduces new
possibilities for solving the supersymmetric flavor problem, the gaugino mass
problem, the supersymmetric CP problem, and the mu-problem. Furthermore, the
compactification scale can be consistent with a unification of gauge and
gravitational couplings. We demonstrate these claims in a four-dimensional
effective theory below the compactification scale that incorporates the
relevant features of the underlying higher dimensional theory and the
contribution of the super-Weyl anomaly. Naturalness constraints follow not only
from symmetries but also from the higher dimensional origins of the theory. We
also introduce additional bulk contributions to the MSSM soft masses. This
scenario is very predictive: the gaugino masses, squark masses, and terms
are given in terms of MSSM renormalization group functions.Comment: 42 pages, LateX, references added, corrections added as Eqs. (43, 53
Holographic Domains of Anti-de Sitter Space
An AdS_4 brane embedded in AdS_5 exhibits the novel feature that a
four-dimensional graviton is localized near the brane, but the majority of the
infinite bulk away from the brane where the warp factor diverges does not see
four-dimensional gravity. A naive application of the holographic principle from
the point of view of the four-dimensional observer would lead to a paradox; a
global holographic mapping would require infinite entropy density. In this
paper, we show that this paradox is resolved by the proper covariant
formulation of the holographic principle. This is the first explicit example of
a time-independent metric for which the spacelike formulation of the
holographic principle is manifestly inadequate. Further confirmation of the
correctness of this approach is that light-rays leaving the brane intersect at
the location where we expect four-dimensional gravity to no longer dominate. We
also present a simple method of locating CFT excitations dual to a particle in
the bulk. We find that the holographic image on the brane moves off to infinity
precisely when the particle exits the brane's holographic domain. Our analysis
yields an improved understanding of the physics of the AdS_4/AdS_5 model.Comment: 29 pages, 6 figure
Unification and the Hierarchy from AdS5
In AdS5, the coupling for bulk gauge bosons runs logarithmically, not as a
power law. For this reason, one can preserve perturbative unification of
couplings. Depending on the cutoff, this can occur at a high scale. We discuss
subtleties in the calculation and present a regularization scheme motivated by
the holographic correspondence. We find that generically, as in the standard
model, the couplings almost unify. For specific choices of the cutoff and
number of scalar multiplets, there is good agreement between the measured
couplings and the assumption of high scale unification.Comment: 5 pages, 2 figure
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