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A. S. Cattaneo

Publications and source records attributed to A. S. Cattaneo.

15 recordsLinked to original sources
arXiv2019

Observables in the equivariant A-model

We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: the first one is conjectured to compute the correlators of the A-model with target the Marsden-Weinstein reduced space; in the second one we recover the topological Yang-Mills action coupled with A-model so that the A-model observables are closed under supersymmetry.

hep-th↗
arXiv2007

Coisotropic embeddings in Poisson manifolds

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.

math.SG↗
arXiv1998

Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory

The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $η$ given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang--Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field $η$ can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in details.

hep-th↗
arXiv1998

Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.

math.DG↗
arXiv1997

BRST Symmetries for the Tangent Gauge Group

For any principal bundle $P$, one can consider the subspace of the space of connections on its tangent bundle $TP$ given by the tangent bundle $T{\cal A}$ of the space of connections ${\cal A}$ on $P$. The tangent gauge group acts freely on $T{\cal A}$. Appropriate BRST operators are introduced for quantum field theories that include as fields elements of $T{\cal A}$, as well as tangent vectors to the space of curvatures. As the simplest application, the BRST symmetry of the so-called $BF$-Yang-Mills theory is described and the relevant gauge fixing conditions are analyzed. A brief account on the topological $BF$ theories is also included and the relevant Batalin-Vilkovisky operator is described.

hep-th↗
arXiv1997

Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.

dg-ga↗
arXiv1994

1D-Disordered Conductor with Loops Immersed in a Magnetic Field

We investigate the conductance of a 1-D disordered conducting loop with two contacts, immersed in a magnetic flux. We show the appearance in this model of the Al'tshuler-Aronov-Spivak behaviour. We also investigate the case of a chain of loops distributed with finite density: in this case we show that the interference effects due to the presence of the loops can lead to the delocalization of the wave function.

cond-mat↗
arXiv1994

Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models

We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains $γ\in H_1(C,\zet_k)$. We make a minimal extension of the resulting models by adding a kinetic term, and we get a new matrix model which realizes a simple dynamics of $\zet_k$-chains on surfaces. This gives a representation of $c=1$ matter coupled to two-dimensional quantum gravity with the target space being a circle of finite radius, as studied by Gross and Klebanov.

hep-th↗
arXiv1993

A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix

In this paper we investigate in more detail our previous formulation of the dilaton-gravity theory by Bilal--Callan--de~Alwis as a $SL_2$-conformal affine Toda (CAT) theory. Our main results are: i) a field redefinition of the CAT-basis in terms of which it is possible to get the black hole solutions already known in the literature; ii) an investigation the scattering matrix problem for the quantum black hole states. It turns out that there is a range of values of the $N$ free-falling shock matter fields forming the black hole solution, in which the end-point state of the black hole evaporation is a zero temperature regular remnant geometry. It seems that the quantum evolution to this final state is non-unitary, in agreement with Hawking's scenario for the black hole evaporation.

hep-th↗
arXiv1992

Quantum Models of Black Hole Evaporation

The discovery of black-hole evaporation represented in many respects a revolutionary event in scientific world; as such, in giving answers to open questions, it gave rise to new problems part of which are still not resolved. Here we want to make a brief review of such problems and examine some possible solutions. Invited Talk at the "Workshop on String Theory, Quantum Gravity and the Unification of the Fundamental Interactions" Rome, September 21-26

hep-th↗
arXiv1992

A Conformal Affine Toda Model of 2D Black Holes: A Quantum Study of the Evaporation End-Point

In this paper we reformulate the dilaton-gravity theory of Callan \etal\ as a new effective conformal field theory which turns out to be a generalization of the so-called $SL_2$-conformal affine Toda (CAT) theory studied some times ago by Babelon and Bonora. We quantize this model, thus keeping in account the dilaton-gravity quantum effects. We then implement a Renormalization Group analysis to study the black hole thermodynamics and the final state of the Hawking evaporation.

hep-th↗