Operator solutions of the bosonized chiral Schwinger model

Starting from the modified Lagrangian of the bosonized chiral Schwinger model, operator solutions are obtained under three types of gauge fixing conditions. We show that the physical spectrum consists of a massive free boson and a massless excitation. We emphasize that the “longitudinal” component of the gauge field must be treated properly.     

Can supersymmetric theories be bosonized?

We investigate the possibility of transforming supersymmetric theories into pure;y fermionic or bosonic forms. The supersymmetric sine-Gordon lagrangian is rewritten in a purely fermionic form, and the Fermi equivalent of the original supersymmetry transformation is derived. This transformation represents an invariance only at the quantum level, when the effects of the chiral anomaly have been taken into account. When supersymmetric theories are written in purely bosonic forms, a non-local bosonic transformation takes place of the supersymmetry transformation. In both cases the supersymmetry algebra, as realized on the fields, is lost.     

Perturbative chiral violations for domain-wall QCD with improved gauge actions

We investigate, in the framework of perturbation theory at finite Ns$N_s$, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained.     

On the renormalization of the bosonized multi-flavor Schwinger model

The phase structure of the bosonized multi-flavor Schwinger model is investigated by means of the differential renormalization group (RG) method. In the limit of small fermion mass the linearized RG flow is sufficient to determine the low-energy behavior of the N  -flavor model, if it has been rotated by a suitable rotation in the internal space. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1$N=1$ or N>1$N>1$, where N   is the number of flavors. For N>1$N>1$ the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1$N=1$ case, where it remains unbroken in the strong coupling phase.     

Gauging Dual Symmetry

For some symmetries the process of transforming from a global to a local symmetry can be achieved by introducing a scalar field rather than a vector field. The symmetry that we study is electric–magnetic dual symmetry which rotates electric and magnetic quantities into one another. Starting from an initial Lagrangian which contains vector fields and satisfies a global electric–magnetic duality, we show that it is possible to make the symmetry local by introducing a scalar field.     

Gauging the conformal group

It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.     

Conformal blocks and correlators in a bosonized WZNW model

The solutions of the Knizhnik-Zamolodchikov equations as conformal blocks of the Wess-Zumino-Novikov-Witten SU(2) model on a sphere are examined. An action that permits finding the N-point correlators of the model, which are constructed in a natural manner from the conformal blocks, is proposed. This is an action of three free fields perturbed by a special marginal operator. The construction described should extend to the case of other groups and surfaces of higher genus. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 10, 648–653 (25 November 1999)     

On Gauging Symmetry of Modular Categories

We develop a non–relativistic twistor theory, in which Newton–Cartan structures of Newtonian gravity correspond to complex three–manifolds with a four–parameter family of rational curves with normal bundle \({\mathcal {O} \oplus \mathcal {O}(2)}\). We show that the Newton–Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton–Cartan connections can nevertheless be reconstructed from Merkulov’s generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non–trivial on twistor lines. The resulting geometries agree with non–relativistic limits of anti-self-dual gravitational instantons.     

Three-reggeon (string) vertex for the Neveu-Schwarz sector with bosonized ghosts

We construct the complete BRST-invariant Sciuto-Della Selva-Saito three-reggeon vertex for the Neveu-Schwarz sector with bosonized reparametrization ghosts and fermionized SUSY ghosts.     

Gauging universe expansion via scalar fields

In this study, we investigate the expansion of the FRLW universe in the open, closed, and flat geometries. The universe is dominated by a scalar field (spatially homogeneous) as a source of dark energy. We consider the three different classes of scalar fields – quintessence, tachyonic, and phantom field – for our analysis. A mathematical analysis is carried out by considering these three scalar fields with exponential and power-law potentials. Both potentials give exponential expansion in the open, closed, and flat FRLW universes. It is found that quintessence, tachyonic, and phantom scalar fields are indistinguishable under the slow roll approximation.     

Gauging a two phase hadron model

We generate a two phase model for hadrons starting from a lagrangian density in terms of quarks and meson fields which extend over all space-time. Our procedure is based on the non-topological soliton approach of Friedberg and Lee. We then apply this scheme to study the coupling of gauge weak bosons, for which the surface is transparent, in a consistent manner.     

Gauging the supersymmetric sigma model with a goldstone field

We gauge the supersymmetric nonlinear sigma model in superspace. We show that the additional terms satisfy a set of Wess-Zumino consistency conditions, and that the vector superfield V plays the role of a Goldstone boson.