arXiv subjects
Publications and source records attributed to A. Lopez.
We study some aspects of recent proposals to use the noncommutative Chern-Simons theory as an effective description of some planar condensed matter models in strong magnetic fields, such as the Quantum Hall Effect. We present an alternative justification for such a description, which may be extended to other planar systems where a uniform magnetic field is present.
We study renormalization effects in the Abelian Chern-Simons (CS) action. These effects can be non-trivial when the gauge field is coupled to dynamical matter, since the regularization of the UV divergences in the model forces the introduction of a parity even piece in the gauge field action. This changes the classical (odd) transformation properties of the pure CS action. This effect, already discussed for the case of a lattice regularization by F. Berruto, M.C. Diamantini and P. Sodano in hep-th/0004203, is also present when the theory is defined in the continuum and, indeed, it is a manifestation of a more general `anomalous' effect, since it happens for every regularization scheme. We explore the physical consequences of this anomaly. We also show that generalized, nonlocal parity transformations can be defined in such a way that the regularized theory is odd, and that those transformations tend to the usual ones when the cutoff is removed. These generalized transformations play a role that is tantamount to the deformed symmetry corresponding to Ginsparg-Wilson fermions [2] (in an even number of spacetime dimensions).
We consider a Dirac field in 2+1 dimensions with a domain wall like defect in its mass, minimally coupled to a dynamical Abelian vector field. The mass of the fermionic field is assumed to have just one linear domain wall, which is externally fixed and unaffected by the dynamics. We show that, under some general conditions on the parameters, the localized zero modes predicted by the Callan and Harvey mechanism are stable under the electromagnetic interaction of the fermions.
We study the transition from the Abelian multi-component (3,3,1) quantum Hall state to the non-Abelian one component Pfaffian state in bilayer two dimensional electron systems. We show that tunneling between layers can induce this transition. At the transition points part of the degrees of freedom that describe the (3,3,1) state disappear from the spectrum, and the system is correctly described by the Pfaffian state, with quasi-particles that satisfy non-Abelian statistics. The mechanism described in this work provides for a physical Hamiltonian interpretation of the algebraic projection from the (3,3,1) to the Pfaffian state that has been discussed in the literature.
We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In the reduced theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein, magnetic flux strings are mapped into domain wall defects. Fermionic zero modes, localized around the flux strings of the 3+1 dimensional theory, become also zero modes in the reduced theory, via the Callan and Harvey mechanism, and are concentrated around the domain wall defects. We also study a dynamical model: massless $QED_4$, with fermions confined to a plane, deriving the effective action that describes the `planar' system.
We study some dynamical properties of a Dirac field in 2+1 dimensions with spacetime dependent domain wall defects. We show that the Callan and Harvey mechanism applies even to the case of defects of arbitrary shape, and in a general state of motion. The resulting chiral zero modes are localized on the worldsheet of the defect, an embedded curved two dimensional manifold. The dynamics of these zero modes is governed by the corresponding induced metric and spin connection. Using known results about determinants and anomalies for fermions on surfaces embedded in higher dimensional spacetimes, we show that the chiral anomaly for this two dimensional theory is responsible for the generation of a current along the defect. We derive the general expression for such a current in terms of the geometry of the defect, and show that it may be interpreted as due to an "inertial" electric field, which can be expressed entirely in terms of the spacetime curvature of the defects. We discuss the application of this framework to fermionic systems with defects in condensed matter.
We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they will be curves lying on the spatial plane. We show how to treat the dynamics of the fermions in such a way that the existence of localized fermionic zero modes on the defects is transparent. Moreover, effects due to the higher, non zero modes, can be quantitatively studied. We also consider the relevance of the profile of the mass near the region where it changes sign. Finally, we apply our general results to the calculation of the induced fermionic current, in the linear response approximation, in the presence of an external electric field and defects.
A hydrodynamic model involving cooling gas in the stagnation region of a collimated outflow is proposed for the formation of the giant parsec-scale bipolar envelope that surrounds the planetary nebula KjPn 8. Analytical calculations and numerical simulations are presented to evaluate the model. The envelope is considered to consist mainly of environmental gas swept-up by shocks driven by an episodic, collimated, bipolar outflow. In this model, which we call the ``free stagnation knot'' mechanism, the swept-up ambient gas located in the stagnation region of the bow-shock cools to produce a high density knot. This knot moves along with the bow-shock. When the central outflow ceases, pressurization of the interior of the envelope stops and its expansion slows down. The stagnation knot, however, has sufficient momentum to propagate freely further along the axis, producing a distinct nose at the end of the lobe. The model is found to successfully reproduce the peculiar shape and global kinematics of the giant bipolar envelope of KjPn 8.
It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality symmetries of toroidally compactified string theory on this system are studied and it is shown that, when the gauge group is compact, the mirror map has the same effect as the Jain map. The extrinsic ingredients of the Jain construction appear naturally as topologically non-trivial field configurations of the compact gauge theory giving a dynamical origin for the Jain hierarchy of fractional quantum Hall states.
Let $S_{g}$ be a general prime K3 surface in $P^g$ of genus $g \geq 3$ or a general double cover of $P^2$ ramified along a sextic curve for $g = 2$ and $S = S_{i,g}$ its {\it i}-th Veronese embedding. In this article we compute the corank of the Gaussian map $Φ:\bigwedge^2 H^0(S,O_S(1)) \to H^0(S,Ω_S^1(2))$ for $i \geq 2, g \geq 2$ and $i=1, g \geq 17$. The main idea is to reduce the surjectivity of $Φ$ to an application of the Kawamata-Viehweg vanishing theorem on the blow-up of $S \times S$ along,the diagonal. This is seen to apply once the hyperplane divisor of the K3 surface $S$ can be decomposed as a sum of three suitable birationally ample divisors. We show that such a decomposition exists when $i \geq 3$ or on some K3 surfaces, constructed using the surjectivity of the period mapping, when $i = 1, g \geq 17$ or $i=2, g \geq 7$.
Whichever could be the real theory of gravitation, the corresponding low-energy effective lagrangian will probably contain higher derivative terms. In this work we study the general conditions on those terms in order to produce enough inflation to solve some of the problems of the standard Friedmann-Robertson-Walker cosmology in absence of any inflaton field. We apply our results to some particular scenarios where higher derivative terms appear in the effective lagrangian for gravity like those coming from graviton (two)-loops or integrating out ordinary matter (like the one present in the Standard Model).
We consider the minimal low-energy action for gravity up to six derivatives which is renormalizable at the two-loop level modulo higher derivative corrections. Then we study the classical solutions corresponding to the Schwarzschild and the Robertson-Walker metrics. In the first case we find a singularity close to the gravitational radius and in the second case we find inflationary de Sitter solutions in absence of any matter or cosmological constant.