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Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is gauge invariant under the grading even bosonic generators. We provide a self-dual notion based on the dual operator. We use the definition of the dual operator to contruct a model with gauge invariance $SO(1,3)\times SU(N) \times U(1) \subset SU(2,2|N)$. The choice of a graded dual operator allows us to overcome technical difficulties of $U(N)$ unified theories based on the superconformal group. The gravity action reproduces the Einstein-Hilbert action in certain sector of the theory. The definition of the dual operator allows us to include fermionic matter in the gauge connection in a geometric manner. We give a summary with possible phenomenological parameters that are included in the model.

We discuss an embedding of $su(n)$ rank-two antisymmetric supercharges in the $su(2,2|d_n)$ superalgebra, where $d_n=n(n-1)/2$. We describe an algorithm to construct the explicit form of the generators of the superalgebra.

We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model., Comment: 27 pages, 1 figure

A background-independent, Lorentz-covariant approach to compute conserved charges in odd-dimensional AdS gravity, alternative to the standard counterterms method, is presented. A set of boundary conditions on the asymptotic extrinsic and Lorentz curvature, rather than a Dirichlet boundary condition on the metric is used. With a given prescription of the boundary term, a well-defined action principle in any odd dimension is obtained. The same boundary term regularizes the Euclidean action and gives the correct black hole thermodynamics. The conserved charges are obtained from the asymptotic symmetries through Noether theorem without reference to any background. For topological AdS black holes the vacuum energy matches the expression conjectured by Emparan, Johnson and Myers \cite{Emparan-Johnson-Myers} for all odd dimensions., Comment: 5 pages, no figures, revtex

A finite action principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term; and is then generalized for arbitrary odd dimensions. The boundary term needed to render the action finite is singled out demanding the action to attain an extremum for an appropriate set of boundary conditions. The boundary term is a local function of the fields at the boundary and is sufficient to render the action finite for asymptotically AdS solutions, without requiring background fields. It is shown that the Euclidean continuation of the action correctly describes the black hole thermodynamics in the canonical ensemble. Additionally, background independent conserved charges associated with the asymptotic symmetries can be written as surface integrals by direct application of Noether's theorem., Comment: Minor changes and references added

Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the degeneracy occurs on domain walls that divide phase space into nonoverlapping regions each one describing a nondegenerate system, causally disconnected from each other. These surfaces are characterized by the sign of the Liouville's flux density on them, behaving as sources or sinks of orbits. In this latter case, once the system reaches the domain wall, it acquires a new gauge invariance and one degree of freedom is dynamically frozen, while the remaining degrees of freedom evolve regularly thereafter., Comment: 6 pages, 1 figure, two columns, revtex. Minor changes. Final version for J. Math. Phys

Asymptotically locally AdS black hole geometries of dimension d > 2 are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer 0 < k < [(d-1)/2] which possess a unique globally AdS vacuum. The transverse sections of these solutions are d-2 surfaces of constant curvature, allowing for different topological configurations. The thermodynamic analysis of these solutions reveals that the presence of a negative cosmological constant is essential to ensure the existence of stable equilibrium states. In addition, it is shown that these theories are holographically related to [(d-1)/2] different conformal field theories at the boundary., Comment: 13 Pages, 3 figures, two columns, Revtex, last version for PRD

New non-perturbatives excitations in the massless Thirring and Schwinger models are discussed., Comment: Revtex, 9pp, to be published in New Trends in Theoretical Physics

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate $x^-$ in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling., Comment: title changed, one reference added, accepted in Phys. Lett. B

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is quantized, and the spin takes a value $n+ 1/2$, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons., Comment: Changed title. To be published in Physics Letters B

It is pointed out that the action recently proposed by Ba\~nados et al. for gravitation in odd dimensions higher (and lower) than four, provides a natural quantization for the gravitational constant. These theories possess no dimensionful parameters and hence they may be power counting renormalizable., Comment: 9 pages, LaTeX