arXiv subjects

A. Restuccia

Publications and source records attributed to A. Restuccia.

At least 91 records · Page 5Linked to original sources

arXiv2001

D-branes, Symplectomorphisms and Noncommutative Gauge Theories

It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A noncommutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theories may be described in terms of symplectic connections on symplectic fibrations. The world volume being its base manifold and the (sub)group of volume preserving diffeomorphisms generate the symplectomorphisms which preserve the (infinite dimensional) Poisson bracket of the fibration.

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arXiv2001

Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories

It is shown that a double compactified D=11 supermembrane with non trivial wrapping may be formulated as a symplectic non-commutative gauge theory on the world volume. The symplectic non commutative structure is intrinsically obtained from the symplectic 2-form on the world volume defined by the minimal configuration of its hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemman surface with a symplectic connection.

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arXiv2000

An Operator Valued Extension of the Super KdV Equations

An extension of the Super KdV integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented. The approach is applied to the above described system and infinitely many conserved quantities are constructed. In a particular case they reduce to the corresponding conserved quantities of Super KdV.

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arXiv2000

Extended Self-Dual Configurations as Stable Exact Solutions in Born-Infeld Theory

A class of exact solutions to the Born-Infeld field equations, over manifolds of any even dimension, is constructed. They are an extension of the self-dual configurations. They are local minima of the action for riemannian base manifolds and local minima of the Hamiltonian for pseudo-riemannian ones. A general explicit expression for the Born-Infeld determinant is obtained, for any dimension of space-time.

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arXiv1999

Stable Solutions of the Double Compactified D=11 Supermembrane Dual

The hamiltonian formulation of the supersymmetric closed 2-brane dual to the double compactified D=11 closed supermembrane is presented. The formulation is in terms of two U(1) vector fields related by the area preserving constraint of the SUSY 2-brane. Stable solutions of the field equations, which are local minima of the hamiltonian, are found. In the semiclassical approximation around the stable solutions the action becomes the reduction of D=10 Super-Maxwell to the worldvolume. The solutions carry RR charges as a type of magnetic charges associated with the worldvolume vector field. The geometrical interpretation of the solution in terms of U(1) line bundles over the worldvolume is obtained.

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arXiv1999

Non Abelian TQFT and scattering of self dual field configuration

A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It is shown that the phase space of the theory can be exactly quantized in terms of the space of holomorphic structures over stable vector bundles of degree zero over Riemann surfaces. The Dirac monopoles are particular static solutions of the field equations. Its relation to topological gravity is discussed.

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arXiv1998

On Some Stability Properties of Compactified D=11 Supermembranes

We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{1}\times S^{1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.

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arXiv1998

On the Interacting Chiral Gauge Field Theory in D=6 and the Off-Shell Equivalence of Dual Born-Infeld-Like Actions

A canonical action describing the interaction of chiral gauge fields in D=6 Minkowski space-time is constructed. In a particular partial gauge fixing it reduces to the action found by Perry and Schwarz. The additional gauge symmetries are used to show the off-shell equivalence of the dimensional reduction to D=5 Minkowski space-time of the chiral gauge field canonical action and the Born-Infeld canonical action describing an interacting D=5 Abelian vector field. Its extension to improve the on-shell equivalence arguments of dual D-brane actions to off-shell ones is discussed.

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arXiv1998

On the QFT relation between Donaldson-Witten invariants and Floer homology theory

A TQFT in terms of general gauge fixing functions is discussed. In a covariant gauge it yields the Donaldson-Witten TQFT. The theory is formulated on a generalized phase space where a simplectic structure is introduced. The Hamiltonian is expressed as the anticommutator of off-shell nilpotent BRST and anti-BRST charges. Following original ideas of Witten a time reversal operation is introduced and an inner product is defined in terms of it. A non-covariant gauge fixing is presented giving rise to a manifestly time reversal invariant Lagrangean and a positive definite Hamiltonian, with the inner product previously introduced. As a consequence, the indefiniteness problem of some of the kinetic terms of the Witten's action is resolved. The construction allows then a consistent interpretation of Floer groups in terms of the cohomology of the BRST charge which is explicitly independent of the background metric. The relation between the BRST cohomology and the ground states of the Hamiltonian is then completely stablished. The topological theories arising from the covariant, Donaldson-Witten, and non-covariant gauge fixing are shown to be quantum equivalent by using the operatorial approach.

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arXiv1998

New Topological Aspects of $BF$ Theories

$BF$ theories defined over non trivial line bundles are studied. It is shown that such theories describe a realization of a non trivial higher order bundle. The partition function differs from the usual one -in terms of the Ray Singer Torsion- by a factor that arises from the non triviality of the line bundles.

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arXiv1997

On the Geometry on Antisymmetric Fields

The geometry of antisymmetric fields with nontrivial transitions over a base manifold is described in terms of exact sequences of cohomology groups. This formulation leads naturally to the appearance of nontrivial topological charges associated to the periods of the curvature of the antisymmetric fields. The relation between the partition functions of dual theories is carefully studied under the most general assumptions, and new topological factors related to zero modes and the Ray Singer torsion are found.

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arXiv1997

On the Stability of Compactified D=11 Supermembranes

We prove D=11 supermembrane theories wrapping around in an irreducible way over $S^{1} \times S^{1}\times M^{9}$ on the target manifold, have a hamiltonian with strict minima and without infinite dimensional valleys at the minima for the bosonic sector. The minima occur at monopole connections of an associated U(1) bundle over topologically non trivial Riemann surfaces of arbitrary genus. Explicit expressions for the minimal connections in terms of membrane maps are presented. The minimal maps and corresponding connections satisfy the BPS condition with half SUSY.

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arXiv1997

Membrane Solitons as Solitary Waves of Non-Linear Strings Dynamics

Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one dimensional extended object. One family of solutions of these equations are solitary waves with several properties of solitonic solutions in integrable systems, giving evidence that in this double dimensional reduction the nonlinear equations are an integrable system. The other family of solutions found, exploits the property that the non linear system under some assumptions is equivalent to a non linear Schr$\ddot {o}$dinger equation.

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arXiv1997

On Global Analysis of Duality Maps

A global analysis of duality transformations is presented. It is shown that duality between quantum field theories exists only when the geometrical structure of the quantum configuration spaces of the theories comply with certain precise conditions. Applications to S-dual actions and to T duality of string theories and D-branes are briefly discussed.It is shown that a new topological term in the dual open string actions is required. We also study an extension of the procedure to construct duality maps among abelian gauge theories to the non abelian case.

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arXiv1997

Duality on Higher Order U(1) Bundles

A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are formulated over these structures. Quantum equivalence is shown between dual theories. A global constraint is proven to be needed to achieve well defined bundles. These global structures are used to refine the proof of the duality equivalence between d=11 supermembrane and d=10 IIA Dirichlet supermembrane, giving a complete topological interpretation to their quantized charges.

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arXiv1996

Non Abelian BF theories with sources and 2-D gravity

We study the interaction of non-Abelian topological $BF$ theories defined on two dimensional manifolds with point sources carrying non-Abelian charges. We identify the most general solution for the field equations on simply and multiply connected two-manifolds. Taking the particular choice of the so-called extended Poincaré group as the gauge group we discuss how recent discussions of two dimensional gravity models do fit in this formalism.

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arXiv1996

BF Topological Theories and Infinitely Reducible Systems

We present a rigurous disscusion for abelian $BF$ theories in which the base manifold of the $U(1)$ bundle is homeomorphic to a Hilbert space. The theory has an infinte number of stages of reducibility. We specify conditions on the base manifold under which the covarinat quantization of the system can be performed unambiguously. Applications of the formulation to the superparticle and the supertstring are also discussed.

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arXiv1996

Magnetic monopoles over topologically non trivial Riemann Surfaces

An explicit canonical construction of monopole connections on non trivial U(1) bundles over Riemann surfaces of any genus is given. The class of monopole solutions depend on the conformal class of the given Riemann surface and a set of integer weights. The reduction of Seiberg-Witten 4-monopole equations to Riemann surfaces is performed. It is shown then that the monopole connections constructed are solutions to these equations.

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