94 research outputs found
Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
In this paper we perform, in the spirit of the holographic correspondence, a
particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a
locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2)
invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory
considered in [Alvarez:2011gd] and featuring "unconventional local
supersymmetry". The model constructed in that reference describes the dynamics
of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to
be relevant for the description of graphene, near the Dirac points, for
specific spatial geometries. Our construction yields the model in
[Alvarez:2011gd] with a specific prescription on the parameters. In this
framework the Dirac spin-1/2 fermion originates from the radial components of
the gravitini in D=4.Comment: 23 page
The Quantum Theory of Chern-Simons Supergravity
We consider -extended Chern-Simons supergravity (\`a la
Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge
symmetries to a BRST symmetry and we perform its quantization by choosing
suitable gauge-fixings. The resulting quantum theories have different features
which we discuss in the present work. In particular, we show that a special
choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez,
Valenzuela and Zanelli for the graphene fermion.Comment: 25 pages. Some points clarified and conclusion section extended;
content of sections 3 and 4 reorganized. Version to be published on JHE
Unbraiding the braided tensor product
We show that the braided tensor product algebra
of two module algebras of a quasitriangular Hopf algebra is
equal to the ordinary tensor product algebra of with a subalgebra of
isomorphic to , provided there exists a
realization of within . In other words, under this assumption we
construct a transformation of generators which `decouples' (i.e.
makes them commuting). We apply the theorem to the braided tensor product
algebras of two or more quantum group covariant quantum spaces, deformed
Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page
A Dynamical 2-dimensional Fuzzy Space
The noncommutative extension of a dynamical 2-dimensional space-time is given
and some of its properties discussed. Wick rotation to euclidean signature
yields a surface which has as commutative limit the doughnut but in a singular
limit in which the radius of the hole tends to zero.Comment: 13 pages, accepted for publication in Phys. Lett.
Deformed quantum mechanics and q-Hermitian operators
Starting on the basis of the non-commutative q-differential calculus, we
introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as
the quantum stochastic counterpart of a generalized classical kinetic equation,
which reproduces at the equilibrium the well-known q-deformed exponential
stationary distribution. In this framework, q-deformed adjoint of an operator
and q-hermitian operator properties occur in a natural way in order to satisfy
the basic quantum mechanics assumptions.Comment: 10 page
Twisting D(2,1; α) Superspace
We develop a three-dimensional N=4 theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets (?I alpha alpha 'alpha?',phi I alpha A) on a curved AdS(3) worldvolume background, whose supersymmetry is captured by the supergroup D2(2,1;alpha). To unveil some remarkable features of this model, we perform two twists, involving the SL(2,R) factors of the theory. After the first twist, our spacetime Lagrangian exhibits a Chern-Simons term associated with an odd one-form field, together with a fermionic "gauge-fixing", in the spirit of the Rozansky-Witten model. The second twist allows to interpret the D2(2,1;alpha) setup as a framework capable of describing massive Dirac particles. In particular, this yields a generalisation of the Alvarez-Valenzuela-Zanelli model of "unconventional supersymmetry". We comment on specific values of the combination alpha+1, which in our model is related to a sort of gauging in the absence of dynamical gauge fields
Quadrupole Instabilities of Relativistic Rotating Membranes
We generalize recent study of the stability of isotropic (spherical) rotating
membranes to the anisotropic ellipsoidal membrane. We find that while the
stability persists for deformations of spin , the quadrupole and higher
spin deformations () lead to instabilities. We find the relevant
instability modes and the corresponding eigenvalues. These indicate that the
ellipsoidal rotating membranes generically decay into finger-like
configurations.Comment: 5 pages, 1 figur
-Extended Supergravity, Unconventional SUSY and Graphene
We derive a dimensional model with unconventional supersymmetry at the
boundary of an -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, and
. The two valleys correspond to the two independent sectors of the
boundary model in the 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 figur
Z-graded differential geometry of quantum plane
In this work, the Z-graded differential geometry of the quantum plane is
constructed. The corresponding quantum Lie algebra and its Hopf algebra
structure are obtained. The dual algebra, i.e. universal enveloping algebra of
the quantum plane is explicitly constructed and an isomorphism between the
quantum Lie algebra and the dual algebra is given.Comment: 17 page
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