No Arabic abstract
Within the context of a bosonized theory, we evaluate the current-current correlation functions corresponding to a massive Dirac field in 2+1 dimensions, which is constrained to a spatial half-plane. We apply the result to the evaluation of induced vacuum currents in the presence of an external field. We comment on the relation with the purely fermionic version of the model, in the large-mass limit.
Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostatic field in various configurations such as step or barrier potentials and generalizations of them. The field is taken as parallel to the y coordinate axis and vanishing outside of a band parallel to the x axis. The classical theory is reviewed, together with its canonical quantization leading to the Dirac equation for a 2-component spinor. Stationary solutions are numerically found for each of the field configurations considered, fromwhich we calculate the mean quantum trajectories of the particle and compare them with the corresponding classical trajectories, the latter showing a classical version of the Klein phenomenon. Transmission and reflection probabilities are also calculated, confirming the Klein phenomenon.
We study the Lorentzian version of the type IIB matrix model as a nonperturbative formulation of superstring theory in (9+1)-dimensions. Monte Carlo results show that not only space but also time emerges dynamically in this model. Furthermore, the real-time dynamics extracted from the matrices turns out to be remarkable: 3 out of 9 spatial directions start to expand at some critical time. This can be interpreted as the birth of our Universe.
We apply the functional bosonization procedure to a massive Dirac field defined on a 2+1 dimensional spacetime which has a non-trivial boundary. We find the form of the bosonized current both for the bulk and boundary modes, showing that the gauge field in the bosonized theory contains a perfect-conductor boundary condition on the worldsheet spanned by the boundary. We find the bononized action for the corresponding boundary modes.
In this paper we construct a $(2,2)$ dimensional string theory with manifest $N=1$ spacetime supersymmetry. We use Berkovits approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The worldsheet symmetry algebra is a twisted and truncated ``small $N=4$ superconformal algebra. The physical spectrum of the open string contains an infinite number of massless states, including a supermultiplet of a self-dual Yang-Mills field and a right-handed spinor and a supermultiplet of an anti-self-dual Yang-Mills field and a left-handed spinor. The higher-spin multiplets are natural generalisations of these self-dual and anti-self-dual multiplets.
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $varepsilon$-expansion.