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

Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons

A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2) invariant formulation where the (effective) horizon degrees of freedom are described by an SU(2) Chern-Simons theory. This leads to a more transparent description of the quantum theory in the context of loop quantum gravity and modifications of the form of the horizon entropy.Comment: 30 pages, 1 figur