The structure of parafermion vertex operator algebras

It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k coincides with a certain W-algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.Comment: 12 page

Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover SL_2(Z)-invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain `odd traces' on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional SL_2(Z)-invariant space. We close the paper with several examples.Comment: 42 pages. Published versio

The economical 3-3-1 model revisited

We show that the economical 3-3-1 model poses a very high new physics scale of the order of 1000~TeV due to the constraint on the flavor-changing neutral current. The implications of the model for neutrino masses, inflation, leptogenesis, and superheavy dark matter are newly recognized. Alternatively, we modify the model by rearranging the third quark generation differently from the first two quark generations, as well as changing the scalar sector. The resultant model now predicts a consistent new physics at TeV scale unlike the previous case and may be fully probed at the current colliders. Particularly, due to the minimal particle contents, the models under consideration manifestly accommodate dark matter candidates and neutrino masses, with novel and distinct production mechanisms. The large flavor-changing neutral currents that come from the ordinary and exotic quark mixings can be avoided due to the approximate $B-L$ symmetry.Comment: 21 pages; english writing improved, dark matter stability stated, and references added; matches journal versio

Effect of the Kondo correlation on thermopower in a Quantum Dot

In this paper we study the thermopower of a quantum dot connected to two leads in the presence of Kondo correlation by employing a modified second-order perturbation scheme at nonequilibrium. A simple scheme, Ng's ansatz [Phys. Rev. Lett. {\bf 76}, 487 (1996)], is adopted to calculate nonequilibrium distribution Green's function and its validity is further checked with regard to the Onsager relation. Numerical results demonstrate that the sign of the thermopower can be changed by tuning the energy level of the quantum dot, leading to a oscillatory behavior with a suppressed magnitude due to the Kondo effect. We also calculate the thermal conductance of the system, and find that the Wiedemann-Franz law is obeyed at low temperature but violated with increasing temperature, corresponding to emerging and quenching of the Kondo effect.Comment: 6 pages, 4 figures; accepted for publication in J Phys.: Condensed Matte

Periodicities in the occurrence of aurora as indicators of solar variability

A compilation of records of the aurora observed in China from the Time of the Legends (2000 - 3000 B.C.) to the mid-18th century has been used to infer the frequencies and strengths of solar activity prior to modern times. A merging of this analysis with auroral and solar activity patterns during the last 200 years provides basically continuous information about solar activity during the last 2000 years. The results show periodicities in solar activity that contain average components with a long period (approx. 412 years), three middle periods (approx. 38 years, approx. 77 years, and approx. 130 years), and the well known short period (approx. 11 years)