242 research outputs found
Quasinormal modes prefer supersymmetry ?
One ambiguity in loop quantum gravity is the appearance of a free parameter
which is called Immirzi parameter. Recently Dreyer has argued that this
parameter may be fixed by considering the quasinormal mode spectrum of black
holes, while at the price of changing the gauge group to SO(3) rather than the
original one SU(2). Physically such a replacement is not quite natural or
desirable. In this paper we study the relationship between the black hole
entropy and the quasi normal mode spectrum in the loop quantization of N=1
supergravity. We find that a single value of the Immirzi parameter agrees with
the semiclassical expectations as well. But in this case the lowest
supersymmetric representation dominates, fitting well with the result based on
statistical consideration. This suggests that, so long as fermions are included
in the theory, supersymemtry may be favored for the consistency of the low
energy limit of loop quantum gravity.Comment: 3 page
Light-cone Gauge NSR Strings in Noncritical Dimensions II -- Ramond Sector
Light-cone gauge superstring theory in noncritical dimensions corresponds to
a worldsheet theory with nonstandard longitudinal part in the conformal gauge.
The longitudinal part of the worldsheet theory is a superconformal field theory
called X^{\pm} CFT. We show that the X^{\pm} CFT combined with the
super-reparametrization ghost system can be described by free variables. It is
possible to express the correlation functions in terms of these free variables.
Bosonizing the free variables, we construct the spin fields and BRST invariant
vertex operators for the Ramond sector in the conformal gauge formulation. By
using these vertex operators, we can rewrite the tree amplitudes of the
noncritical light-cone gauge string field theory, with external lines in the
(R,R) sector as well as those in the (NS,NS) sector, in a BRST invariant way.Comment: 33 pages; v2: minor modification
Supersymmetry algebra in N = 1 chiral supergravity
We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian
for supergravity (SUGRA) with the complex tetrad following the method
used in the usual SUGRA, and present the explicit form of the SUSY
trasformations in the first-order form. The SUSY transformations are generated
by two independent Majorana spinor parameters, which are apparently different
from the constrained parameters employed in the method of the 2-form gravity.
We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late
N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density
We obtain N = 3 chiral supergravity (SUGRA) compatible with the reality
condition by applying the prescription of constructing the chiral Lagrangian
density from the usual SUGRA. The chiral Lagrangian density in
first-order form, which leads to the Ashtekar's canonical formulation, is
determined so that it reproduces the second-order Lagrangian density of the
usual SUGRA especially by adding appropriate four-fermion contact terms. We
show that the four-fermion contact terms added in the first-order chiral
Lagrangian density are the non-minimal terms required from the invariance under
first-order supersymmetry transformations. We also discuss the case of higher N
theories, especially for N = 4 and N = 8.Comment: 20 pages, Latex, some more discussions and new references added, some
typos corrected, accepted for publication in Physical Review
Anti-self-dual Maxwell solutions on hyperk\"ahler manifold and N=2 supersymmetric Ashtekar gravity
Anti-self-dual (ASD) Maxwell solutions on 4-dimensional hyperk\"ahler
manifolds are constructed. The N=2 supersymmetric half-flat equations are
derived in the context of the Ashtekar formulation of N=2 supergravity. These
equations show that the ASD Maxwell solutions have a direct connection with the
solutions of the reduced N=2 supersymmetric ASD Yang-Mills equations with a
special choice of gauge group. Two examples of the Maxwell solutions are
presented.Comment: 9 page
Minimal Off-Shell Version of N = 1 Chiral Supergravity
We construct the minimal off-shell formulation of N = 1 chiral supergravity
(SUGRA) introducing a complex antisymmetric tensor field and a
complex axial-vector field as auxiliary fields. The resulting algebra
of the right- and left-handed supersymmetry (SUSY) transformations closes off
shell and generates chiral gauge transforamtions and vector gauge
transformations in addition to the transformations which appear in the case
without auxiliary fields.Comment: 9 pages, late
Canonical formulation of N = 2 supergravity in terms of the Ashtekar variable
We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity
(SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following
the method employed in the usual SUGRA. In order to get the full graded algebra
of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we
extend the internal, global O(2) invariance to local one by introducing a
cosmological constant to the chiral Lagrangian. The resultant Lagrangian does
not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY
transformation parameters are not constrained at all. We derive the canonical
formulation of the N = 2 theory in such a manner as the relation with the usual
SUGRA be explicit at least in classical level, and show that the algebra of the
Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra,
G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated
with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in
a simple form in terms of these variables. We quantize the theory in the
graded-connection representation and discuss the solutions of quantum
constraints.Comment: 19 pages, Latex, corrected some typos and added a referenc
Holographic Formulation of Quantum Supergravity
We show that supergravity with a cosmological constant can be
expressed as constrained topological field theory based on the supergroup
. The theory is then extended to include timelike boundaries with
finite spatial area. Consistent boundary conditions are found which induce a
boundary theory based on a supersymmetric Chern-Simons theory. The boundary
state space is constructed from states of the boundary supersymmetric
Chern-Simons theory on the punctured two sphere and naturally satisfies the
Bekenstein bound, where area is measured by the area operator of quantum
supergravity.Comment: 30 pages, no figur
Local time and the pricing of time-dependent barrier options
A time-dependent double-barrier option is a derivative security that delivers
the terminal value at expiry if neither of the continuous
time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time
interval . Using a probabilistic approach we obtain a decomposition of
the barrier option price into the corresponding European option price minus the
barrier premium for a wide class of payoff functions , barrier functions
and linear diffusions . We show that the barrier
premium can be expressed as a sum of integrals along the barriers of
the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair
of functions solves a system of Volterra integral
equations of the first kind. We find a semi-analytic solution for this system
in the case of constant double barriers and briefly discus a numerical
algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic
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