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A. Restuccia

Publications and source records attributed to A. Restuccia.

At least 55 records · Page 3Linked to original sources
arXiv2010

A N=8 action for multiple M2-branes with an arbitrary number of colors

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes. We analyze also other limits of the theory: when M goes to we obtain a condensate of M2-branes. If we consider, instead of the exact action, its matrix regularized version, for suitable large N but with a finite number of colors, the algebra of the first class-constraints also closes with the ordinary product and we obtain a regularized 2+1D SU(M) SYM theory in the IR phase that is coupled to the SU(N) regularized supermembrane action. The supersymmetric regularized theory with the ordinary product has purely discrete spectrum. Our theory with the star-product is a full-fledged description of multiple M2-branes minimally immersed in distinction with other constructions that represent multiple M2-branes in the low energy approximation.

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arXiv2009

Non-abelian D=11 Supermembrane

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes.

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arXiv2008

Infinite sequence of new conserved quantities for N=1 SKdV and the supersymmetric cohomology

An infinite sequence of new non-local conserved quantities for N=1 Super KdV (SKdV) equation is obtained. The sequence is constructed, via a Gardner trasformation, from a new conserved quantity of the Super Gardner equation. The SUSY generator defines a nilpotent operation from the space of all conserved quantities into itself. On the ring of $C_\downarrow^\infty$ superfields the local conserved quantities are closed but not exact. However on the ring of $C_{NL,1}^\infty$ superfields, an extension of the $C_\downarrow^\infty$ ring, they become exact and equal to the SUSY transformed of the subset of odd non-local conserved quantities of the appropriate weight. The remaining odd no-local ones generate closed geometrical objects which become exact when the ring is extended to the $C_{NL,2}^\infty$ superfields and equal to the SUSY transformed of the new even non-local conserved quantities we have obtained. These ones fit exactly in the SUSY cohomology of the already known conserved quantities.

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arXiv2008

The Supermembrane with Central Charges on a G2 Manifold

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2 orbifold construction. The hamiltonian H of the theory on a T7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N=1 supersymmetry.

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arXiv2008

Noncommutative associative superproduct for general supersymplectic forms

We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantization a la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincare symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories.

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arXiv2008

N=1 4D Supermembrane from 11D

The action of the 11D supermembrane with nontrivial central charges compactified on a 7D toroidal manifold is obtained. It describes a supermembrane evolving in a 4d Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters.

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arXiv2008

The Minimally Immersed 4D Supermembrane

In this note we summarize some of the properties found in [1], and its relation with [2]. We comment on the construction of the action of the 11D supermembrane with nontrivial central charges minimally immersed on a 7D toroidal manifold is obtained (MIM2).The transverse coordinates to the supermembrane are maps to a 4D Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a 11D Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters. Moreover due to the discrete symmetries of the hamiltonian, there are only 7 possible minimal holomorphic immersions of the MIM2 on the 7-torus. When these symmetries are identified on the target space, it corresponds to compactify the MIM2 on a orbifold with G2 structure. Once the singularities are resolved it leads to the compactification of the MIM2 on a G2 manifold as shown in [2].

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arXiv2008

Nonperturbative SL(2,Z) (p,q)-strings manifestly realized on the quantum M2

The SL(2,Z) duality symmetry of IIB superstring is naturally realized on the D=11 supermembrane restricted to have central charges arising from a nontrivial wrapping. This supermembrane is minimally immersed on the target space (MIM2). The hamiltonian of the MIM2 has a discrete quantum spectrum. It is manifestly invariant under the SL(2,Z) symmetry associated to the conformal symmetry on the base manifold and under a SL(2,Z) symmetry on the moduli of the target space. The mass contribution of the string states on the MIM2 is obtained by freezing the remaining degrees of freedom. It exactly agrees with the perturbative spectrum of the (p,q) IIB and IIA superstring compactified on a circle. We also construct a MIM2 in terms of a dual target space, then a (p,q) set of non-perturbative states associated to the IIA superstring is obtained.

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arXiv2007

The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition

The spectrum of the bosonic sector of the D=11 supermembrane with central charges is shown to be discrete and with finite multiplicities, hence containing a mass gap. The result extends to the exact theory our previous proof of the similar property for the SU(N) regularised model and strongly suggest discreteness of the spectrum for the complete Hamiltonian of the supermembrane with central charges. This theory is a quantum equivalent to a symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the space-like sector is a Riemann surface of positive genus. In this context, it is argued how the theory in 4D exhibits confinement in the N=1 supermembrane with central charges phase and how the theory enters in the quark-gluon plasma phase through the spontaneous breaking of the centre. This phase is interpreted in terms of the compactified supermembrane without central charges.

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arXiv2007

The discrete spectrum of the D=11 bosonic M5-brane

We prove that the spectrum of the regularized M5-brane in D=11 target space is discrete with eigenvalues extending to infinity. The proof includes the same result for the spectra of regularized bosonic p-branes in general.

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arXiv2007

New non-local SUSY KdV conservation laws from a recursive gradient algorithm

A complete proof of the recursive gradient approach is presented. It gives a construction of all the hierarchy structures of N=1 Super KdV, including the non-local one. A precise definition of the ring of superfields involved in the non-local construction is given. In particular, new non-local conserved quantities of N=1 Super KdV are found.

hep-th↗
arXiv2007

Quantum algebra of $N$ superspace

We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace both in the case where there are not central charges in the algebra and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges we present the equivalent results when the central charge and the mass are different. For the kappa-symmetric case when these quantities are equal we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

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arXiv2007

Exact discretness and mass gap of N=1 symplectic Yang-Mills from M-theory

In this note we summarize some of the results found recently in hep-th/0609054. We show the pure discretness of the non-perturbative quantum spectrum of a symplectic Yang-Mills theory defined on a Riemann surface of positive genus, living in a target space that, in particular, can be 4D. This theory corresponds to the membrane with central charges. The presence of the central charge induces a confinement in the phase at zero temperature. When the energy rises, the center of the group breaks and the theory enters in a quark-plasma phase after a topological transition, corresponding to the N=4 wrapped supermembrane.

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arXiv2006

Intrinsic Moment of Inertia of Membranes as bounds for the mass gap of Yang-Mills Theories

We obtain the precise condition on the potentials of Yang-Mills theories in 0+1 dimensions and D0 brane quantum mechanics ensuring the discretness of the spectrum. It is given in terms of a moment of inertia of the membrane. From it we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the slow-mode regime. In particular we analyze the physical case D=3. The quantum mechanical behavior of the theories, concerning its spectrum, is determined by harmonic oscillators with frequencies given by the inertial tensor of the membrane. We find a class of quantum mechanic potential polynomials of any degree, with classical instabilities that at quantum level have purely discrete spectrum.

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arXiv2006

On the Quantization of Massive Superparticles

We consider the action of the D=11 supermembrane wrapping a compactified sector of the target space in such a way that a non trivial central charge in the SUSY algebra is induced. We show that the dynamics of the center of mass corresponds to a superparticle in D=9 with additional fermionic terms associated to the central charges . We perform the covariant quantization of this system following a direct approach which introduces an equivalent action for the system which has only first class constraints allowing to obtain the space of physical states in a covariant way. The resulting multiplet contains $2^8$ states corresponding to a $KKB$ ultrashort multiplet.

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arXiv2006

Interacting D2-branes in 10 dimensions and non abelian Born-Infeld theory

In this paper we extend the bosonic $D$-brane action in D=10 obtained by duality from the D=11 membrane wrapped on $S^1$ to an SU(2) non abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the $D2$-brane to include non abelian symmetry generators. From the SU(2) $D$-brane action, we also obtain the SU(2) Born-Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyze non-abelian Born-Infeld theories.

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arXiv2006

Superprojectors in D=10

We classify all massive irreducible representations of super Poincaré in D=10. New Casimir operators of super Poincaré are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains three irreducible representations of massive supersymmetry and we find the corresponding superprojectors. We apply these new tools to the quantization of the massive superparticle and we show that it must be formulated in terms of a superfield $B_\mn$ satisfying an adequate covariant restriction.

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arXiv2006

The quantum algebra of superspace

We present the complete set of $N=1$, $D=4$ quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, anti-chiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are non-commuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the anti-chiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.

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