arXiv subjects

Francesco Toppan

Publications and source records attributed to Francesco Toppan.

66 records · Page 4Linked to original sources

arXiv2003

On the Octonionic M-superalgebra

The generalized supersymmetries admitting abelian bosonic tensorial central charges are classified in accordance with their division algebra structure (over ${\bf R}$, ${\bf C}$, ${\bf H}$ or ${\bf O}$). It is shown in particular that in D=11 dimensions, the $M$-superalgebra admits a consistent octonionic formulation, involving 52 real bosonic generators (in place of the 528 of the standard $M$-superalgebra). The octonionic $M5$ (super-5-brane) sector coincides with the octonionic $M1$ and $M2$ sectors, while in the standard formulation these sectors are all independent. The octonionic conformal and superconformal $M$-algebras are explicitly constructed. They are respectively given by the $Sp(8|{\bf O})$ ($OSp(1,8|{\bf O})$) (super)algebra of octonionic-valued (super)matrices, whose bosonic subalgebra consists of 232 (and respectively 239) generators.

hep-th↗

arXiv2002

On anomalies in classical dynamical systems

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure, close an algebra which is just the centrally extended version of the original symmetry algebra. The consistency conditions for this to occur are derived. Explicit examples are given based on simple two-dimensional models. Applications of the above scheme and lines of further investigations are suggested.

math-ph↗

arXiv2002

Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory

We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are described for D=4 by OSp(1;8| R), for D=5 by SU(4,4;1) and for D=7 by U_αU(8;1|H). The relation with other schemes, in particular the framework of conformal spin (super)algebras and Jordan (super)algebras is discussed. By extending the division-algebra-valued superalgebras to octonions we get in D=11 an octonionic generalized Poincare superalgebra, which we call octonionic M-algebra, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure, only 52 real bosonic generators remain independent in place of the 528 bosonic charges of standard M-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-5-brane) sectors. We also define the octonionic generalized conformal M-superalgebra, with 239 bosonic generators.

hep-th↗

arXiv2000

Triality of Majorana-Weyl Spacetimes with Different Signatures

Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. This corresponds to a very fundamental property of the supersymmetry in higher dimensions, i.e. that any given theory can be formulated in different signatures all interconnected by the S_3 permutation group.

hep-th↗

arXiv1998

Super-Affine Hierarchies and their Poisson Embeddings

The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for constructing matrix-type Lax operators, which makes the supersymmetric case essentially different from the bosonic counterpart, is overcome via the notion of Poisson embeddings (P.E.), i.e. Poisson mappings relating affine structures to conformal structures (in their simplest version P.E. coincide with the Sugawara construction). A full class of hierarchies can be recovered by using uniquely Lie-algebraic notions. The group-algebraic properties implicit in the super-affine picture allow a systematic derivation of reduced hierarchies by imposing either coset conditions or hamiltonian constraints (or possibly both).

hep-th↗

arXiv1997

Susy Hierarchies and Affine Algebras

We review some basic features of the Lie-algebraic classification of W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out the role of affine Lie algebras. We emphasize that the supersymmetric extensions of the above construction possibly lead, though some questions are still opened, to the classification of supersymmetric hierarchies based on ``generic'' supersymmetric affine Lie algebras. Here the word generic is used to make clear that well-known procedures, as those introduced by Inami and Kanno, are too restricted and do not lead to the full spectrum of supersymmetric integrable hierarchies one can construct. A particular attention is devoted to the large-N supersymmetric extensions (here N=4). The attention paid by large-N theories being due to the fact that they arise as dimensional reduction of N=1 models, and moreover that they realize an ``unification'' of known hierarchies.

solv-int↗

arXiv1996

An n=(1|1) super--Toda Model Based on OSp(1|4)

We show that a Hamiltonian reduction of affine Lie superalgebras having bosonic simple roots (such as $OSp(1|4)$) ``does'' produce supersymmetric Toda models, with superconformal symmetry being nonlinearly realised for those fields of the Toda system which are related to the bosonic simple roots of the superalgebra. A fermionic $b-c$ system of conformal spin $(3/2,-1/2)$ is a natural ingredient of such models.

hep-th↗

arXiv1996

Hamiltonian Reduction of Supersymmetric WZNW Models on Bosonic Groups and Superstrings

It is shown that an alternative supersymmetric version of the Liouville equation extracted from D=3 Green-Schwarz superstring equations naturally arises as a super-Toda model obtained from a properly constrained supersymmetric WZNW theory based on the $sl(2, R)$ algebra. Hamiltonian reduction is performed by imposing a nonlinear superfield constraint which turns out to be a mixture of a first- and second-class constraint on supercurrent components. Supersymmetry of the model is realized nonlinearly and is spontaneously broken. The set of independent current fields which survive the Hamiltonian reduction contains (in the holomorphic sector) one bosonic current of spin 2 (the stress--tensor of the spin 0 Liouville mode) and two fermionic fields of spin ${3/2}$ and $-1/2$. The $n=1$ superconformal system thus obtained is of the same kind as one describing noncritical fermionic strings in a universal string theory. The generalization of this procedure allows one to produce from any bosonic Lie algebra super--Toda models and associated super-W algebras together with their nonstandard realizations.

hep-th↗

arXiv1996

On "Bosonic, Fermionic and Mixed" Supersymmetric 2-Dimensional Integrable Models

It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given by superaffinizations of any bosonic Lie or any super-Lie algebra. This result allows enlarging the set of supersymmetric integrable models, which are no longer restricted to the subclass of superaffinizations of purely fermionic super-Lie algebras (that is admitting fermionic simple roots only).

hep-th↗

arXiv1995

On Matrix KP and Super-KP Hierarchies in the Homogeneous Grading

Constrained KP and super-KP hierarchies of integrable equations (generalized NLS hierarchies) are systematically produced through a Lie algebraic AKS-matrix framework associated to the homogeneous grading. The role played by different regular elements to define the corresponding hierarchies is analyzed as well as the symmetry properties under the Weyl group transformations. The coset structure of higher order hamiltonian densities is proven.\par For a generic Lie algebra the hierarchies here considered are integrable and essentially dependent on continuous free parameters. The bosonic hierarchies studied in \cite{{FK},{AGZ}} are obtained as special limit restrictions on hermitian symmetric-spaces.\par In the supersymmetric case the homogeneous grading is introduced consistently by using alternating sums of bosons and fermions in the spectral parameter power series.\par The bosonic hierarchies obtained from ${\hat {sl(3)}}$ and the supersymmetric ones derived from the $N=1$ affinization of $sl(2)$, $sl(3)$ and $osp(1|2)$ are explicitly constructed. \par An unexpected result is found: only a restricted subclass of the $sl(3)$ bosonic hierarchies can be supersymmetrically extended while preserving integrability.

hep-th↗

arXiv1994

N=1,2 Super-NLS Hierarchies as Super-KP Coset Reductions

We define consistent finite-superfields reductions of the $N=1,2$ super-KP hierarchies via the coset approach we already developped for reducing the bosonic KP-hierarchy (generating e.g. the NLS hierarchy from the $sl(2)/U(1)-{\cal KM}$ coset). We work in a manifestly supersymmetric framework and illustrate our method by treating explicitly the $N=1,2$ super-NLS hierarchies. W.r.t. the bosonic case the ordinary covariant derivative is now replaced by a spinorial one containing a spin ${\textstyle {1\over 2}}$ superfield. Each coset reduction is associated to a rational super-$\cw$ algebra encoding a non-linear super-$\cw_\infty$ algebra structure. In the $N=2$ case two conjugate sets of superLax operators, equations of motion and infinite hamiltonians in involution are derived. Modified hierarchies are obtained from the original ones via free-fields mappings (just as a m-NLS equation arises by representing the $sl(2)-{\cal KM}$ algebra through the classical Wakimoto free-fields).

hep-th↗

arXiv1993

Generalized NLS Hierarchies from Rational $W$ Algebras

Finite rational $\cw$ algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. In this letter we address the problem of relating these algebras to integrable hierarchies of equations, by showing how to associate to a rational $\cw$ algebra its corresponding hierarchy. We work out two examples: the $sl(2)/U(1)$ coset, leading to the Non-Linear Schrödinger hierarchy, and the $U(1)$ coset of the Polyakov-Bershadsky $\cw$ algebra, leading to a $3$-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies.

hep-th↗