404 research outputs found

### Loop Equations and the Topological Phase of Multi-Cut Matrix Models

We study the double scaling limit of mKdV type, realized in the two-cut
Hermitian matrix model. Building on the work of Periwal and Shevitz and of
Nappi, we find an exact solution including all odd scaling operators, in terms
of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop
equations which can be expressed as Virasoro constraints on the partition
function. We discover a ``pure topological" phase of the theory in which all
correlation functions are determined by recursion relations. We also examine
macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to
dense polymers.Comment: 24p

### Covariant canonical formalism for four-dimensional BF theory

The covariant canonical formalism for four-dimensional BF theory is
performed. The aim of the paper is to understand in the context of the
covariant canonical formalism both the reducibility that some first class
constraints have in Dirac's canonical analysis and also the role that
topological terms play. The analysis includes also the cases when both a
cosmological constant and the second Chern character are added to the pure BF
action. In the case of the BF theory supplemented with the second Chern
character, the presymplectic 3-form is different to the one of the BF theory in
spite of the fact both theories have the same equations of motion while on the
space of solutions they both agree to each other. Moreover, the analysis of the
degenerate directions shows some differences between diffeomorphisms and
internal gauge symmetries.Comment: Latex file, 22 pages (due to the macro). Revised version to match
published versio

### Covariant Symplectic Structure and Conserved Charges of New Massive Gravity

We show that the symplectic current obtained from the boundary term, which
arises in the first variation of a local diffeomorphism invariant action, is
covariantly conserved for any gravity theory described by that action.
Therefore, a Poincare invariant 2-form can be constructed on the phase space,
which is shown to be closed without reference to a specific theory. Finally, we
show that one can obtain a charge expression for gravity theories in various
dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for
spacetimes with non-constant curvature backgrounds, by using the diffeomorphism
invariance of the symplectic 2-form. As an example, we calculate the conserved
charges of some solutions of New Massive Gravity (NMG) and compare the results
with the previous works.Comment: 18 pages, No figures, RevTEX4.1; ver 2: minor corrections, version
accepted for publication in Physical Review

### A Covariant Approach To Ashtekar's Canonical Gravity

A Lorentz and general co-ordinate co-variant form of canonical gravity, using
Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic
and Witten is used, in which a point in phase space represents a solution of
the equations of motion and a symplectic functional two form is constructed
which is Lorentz and general co-ordinate invariant. The subtleties and
difficulties due to the complex nature of Ashtekar's variables are addressed
and resolved.Comment: 18 pages, Plain Te

### Counting Giant Gravitons in AdS_3

We quantize the set of all quarter BPS brane probe solutions in global AdS_3
\times S^3 \times T^4/K3 found in arxiv:0709.1168 [hep-th]. We show that,
generically, these solutions give rise to states in discrete representations of
the SL(2,R) WZW model on AdS_3. Our procedure provides us with a detailed
description of the low energy 1/4 and 1/2 BPS sectors of string theory on this
background. The 1/4 BPS partition function jumps as we move off the point in
moduli space where the bulk theta angle and NS-NS fields vanish. We show that
generic 1/2 BPS states are protected because they correspond to geodesics
rather than puffed up branes. By exactly quantizing the simplest of the probes
above, we verify our description of 1/4 BPS states and find agreement with the
known spectrum of 1/2 BPS states of the boundary theory. We also consider the
contribution of these probes to the elliptic genus and discuss puzzles, and
their possible resolutions, in reproducing the elliptic genus of the symmetric
product.Comment: 47 pages; (v2) references and minor clarifications adde

### A topological limit of gravity admitting an SU(2) connection formulation

We study the Hamiltonian formulation of the generally covariant theory
defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad
field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This
theory can be thought of as the limit of the Holst action for gravity for the
Newton constant G goes to infinity and Immirzi parameter goes to zero, while
keeping their product fixed. This theory has for a long time been conjectured
to be topological. We prove this statement both in the covariant phase space
formulation as well as in the standard Dirac formulation. In the time gauge,
the unconstrained phase space of theory admits an SU(2) connection formulation
which makes it isomorphic to the unconstrained phase space of gravity in terms
of Ashtekar-Barbero variables. Among possible physical applications, we argue
that the quantization of this topological theory might shed new light on the
nature of the degrees of freedom that are responsible for black entropy in loop
quantum gravity.Comment: Appendix added where moldels leading to boundary degrees of freedom
are constructed. This version will appear in PRD

### Modeling Life as Cognitive Info-Computation

This article presents a naturalist approach to cognition understood as a
network of info-computational, autopoietic processes in living systems. It
provides a conceptual framework for the unified view of cognition as evolved
from the simplest to the most complex organisms, based on new empirical and
theoretical results. It addresses three fundamental questions: what cognition
is, how cognition works and what cognition does at different levels of
complexity of living organisms. By explicating the info-computational character
of cognition, its evolution, agent-dependency and generative mechanisms we can
better understand its life-sustaining and life-propagating role. The
info-computational approach contributes to rethinking cognition as a process of
natural computation in living beings that can be applied for cognitive
computation in artificial systems.Comment: Manuscript submitted to Computability in Europe CiE 201

### A realisation of Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime,
characterised by a constant vector, can be made invariant under infinitesimal
Lorentz transformations by restricting the allowed field configurations. These
restricted fields are defined as functions of the background vector in such a
way that background dependance of the dynamics of the physical system is no
longer manifest. We show here that they also provide a field basis for the
realisation of Lorentz algebra and allow the construction of a Poincar\'e
invariant symplectic two form on the covariant phase space of the theory.Comment: text body edited, reference adde

### On The Reduced Canonical Quantization Of The Induced 2D-Gravity

The quantization of the induced 2d-gravity on a compact spatial section is
carried out in three different ways. In the three approaches the supermomentum
constraint is solved at the classical level but they differ in the way the
hamiltonian constraint is imposed. We compare these approaches establishing an
isomorphism between the resulting Hilbert spaces.Comment: 17 pages, plain LaTeX. FTUV/93-15, IFIC/93-10, Imperial-TP/93-94/1

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