Quantization of Neveu-Schwarz-Ramond Superstring Model in 10+2-dimensional Spacetime

We construct a Neveu-Schwarz-Ramond superstring model which is invariant under supersymmetric U(1)_V * U(1)_A gauge transformations as well as the super-general coordinate, the super local Lorentz and the super-Weyl transformations on the string world-sheet. We quantize the superstring model by covariant BRST formulation a la Batalin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantizations the model turns out to be formulated consistently in 10+2-dimensional background spacetime involving two time dimensions.Comment: 1+61 pages, no figures, LaTe

Magnetic conductivity and Chern-Simons Term in Holographic Hydrodynamics of Charged AdS Black Hole

We study the effects of the Chern-Simons term in the hydrodynamics of the five-dimensional Reissner-Nordstrom-AdS background. We work out the decoupling problem of the equations of motion and calculate the retarded Green functions explicitly. We then find that the Chern-Simons term induces the magnetic conductivity caused by the anomaly effect. It is increasing function of temperature running from a non-zero value at zero temperature to the twice the value at infinite temperature.Comment: 19 pages, 2 figures; v2 discussion on classification of perturbation fields based on helicity base, third order in dispersion relation and more discussion on magnetic conductivity are added, some typos are corrected and references are added; v3 published versio

Quark Number Susceptibility with Finite Quark Mass in Holographic QCD

We study the effect of a finite quark mass on the quark number susceptibility in the framework of holographic QCD. We work in a bottom-up model with a deformed AdS black hole and D3/D7 model to calculate the quark number susceptibility at finite temperature with/without a finite quark chemical potential. As expected the finite quark mass suppresses the quark number susceptibility. We find that at high temperatures $T\ge 600$ MeV the quark number susceptibility of light quarks and heavy quarks are almost equal in the bottom-up model. This indicates that the heavy quark like charm contribution to thermodynamics of a QCD-like system may start to become significant at temperatures $T\sim 600$ MeV. In D3/D7 model, we focus on the competition between the quark chemical potential, which enhances the quark number susceptibility, and the quark mass that suppresses the susceptibility. We observe that depending on the relative values of the quark mass and the quark chemical potential, the quark number susceptibility shows a diverging or converging behavior. We also calculate the chiral susceptibility in D3/D7 model to support the observation made with the quark number susceptibility.Comment: 16 pages, 3 figure

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture

For quadratic curves over $Q$ in $F_p$, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.Comment: 16 page