218 research outputs found
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
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
Noncommutative Topological Half-flat Gravity
We formulate a noncommutative description of topological half-flat gravity in
four dimensions. BRST symmetry of this topological gravity is deformed through
a twisting of the usual BRST quantization of noncommutative gauge theories.
Finally it is argued that resulting moduli space of instantons is characterized
by the solutions of a noncommutative version of the Plebanski's heavenly
equation.Comment: 12+1 pages, revtex4, no figure
BRST Analysis of Physical States in Two-Dimensional Black Hole
We study the BRST cohomology for coset model, which describes
an exact string black hole solution. It is shown that the physical spectrum
could contain not only the extra discrete states corresponding to those in
two-dimensional gravity but also many additional new states with ghost
number . We also discuss characters for nonunitary
representations and the relation of our results to other approaches.Comment: 44 pages, OS-GE 28-93, OU-HET 17
Gravitational Instantons and Moduli Spaces of Topological 2-form Gravity
A topological version of four-dimensional (Euclidean) Einstein gravity which
we propose regards anti-self-dual 2-forms and an anti-self-dual part of the
frame connections as fundamental fields. The theory describes the moduli spaces
of conformally self-dual Einstein manifolds for the non-zero cosmological
constant case and Einstein-Kahlerian manifold with the vanishing real first
Chern class for the zero cosmological constant. In the non-zero cosmological
constant case, we evaluate the index of the elliptic complex associated with
the moduli space and calculate the partition function. We also clarify the
moduli space and its dimension for the zero cosmological constant case which
are related to the Plebansky's heavenly equations.Comment: 36pages, LaTex, TIT/HEP-247/COSMO-4
Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux
in various dimensions. We realize the backgrounds as supercosets and analyze
explicitly two classes of models: non-critical superstrings on AdS_{2d} and
critical superstrings on AdS_p\times S^p\times CY. We work both in the
Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter
family of flat currents (a Lax connection) leading to an infinite number of
conserved non-local charges, which imply the classical integrability of both
sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove
the quantum integrability of the sigma-model. We discuss how classical
\kappa-symmetry implies one-loop conformal invariance. We consider the addition
of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos
fixed in some equations; v3: typos fixed to match the published versio
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
A candidate for a background independent formulation of M theory
A class of background independent membrane field theories are studied, and
several properties are discovered which suggest that they may play a role in a
background independent form of M theory. The bulk kinematics of these theories
are described in terms of the conformal blocks of an algebra G on all oriented,
finite genus, two-surfaces. The bulk dynamics is described in terms of causal
histories in which time evolution is specified by giving amplitudes to certain
local changes of the states. Holographic observables are defined which live in
finite dimensional states spaces associated with boundaries in spacetime. We
show here that the natural observables in these boundary state spaces are, when
G is chosen to be Spin(D) or a supersymmetric extension of it, generalizations
of matrix model coordinates in D dimensions. In certain cases the bulk dynamics
can be chosen so the matrix model dynamics is recoverd for the boundary
observables. The bosonic and supersymmetric cases in D=3 and D=9 are studied,
and it is shown that the latter is, in a certain limit, related to the matrix
model formulation of M theory. This correspondence gives rise to a conjecture
concerning a background independent form of M theory in terms of which
excitations of the background independent membrane field theory that correspond
to strings and D0 branes are identified.Comment: Latex 46 pages, 21 figures, new results included which lead to a
modification of the statement of the basic conjecture. Presentation improve
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent
theories of quantum spacetime dynamics is defined. The SU(2) spin networks of
quantum general relativity are replaced by labelled compact two-dimensional
surfaces. The space of states of the theory is the direct sum of the spaces of
invariant tensors of a quantum group G_q over all compact (finite genus)
oriented 2-surfaces. The dynamics is background independent and locally causal.
The dynamics constructs histories with discrete features of spacetime geometry
such as causal structure and multifingered time. For SU(2) the theory satisfies
the Bekenstein bound and the holographic hypothesis is recast in this
formalism.Comment: Latex 33 pages, 7 Figure, epsfi
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