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The renormalizability of the three dimensional supersymmetric CP^(N - 1) model is discussed in the 1/N-expansion method, to all orders of 1/N. The model has N copies of the dynamical field and the amplitudes are expanded in powers of 1/N. In order to see the effects of supersymmetry explicitly, Feynman rules for superfields are used. All divergences in amplitudes can be eliminated by the renormalizations of the coupling constant and the wavefunction of the dynamical field to all orders of 1/N. The beta function of the coupling constant is also calculated to all orders of 1/N. It is shown that this model has a non-trivial ultraviolet fixed point. The beta function is shown to have no higher order correction in the 1/N-expansion., Comment: 55 pages, 54 figures; added references

We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the nonperturbative methods, to find the fixed points. Existence of fixed points is extremely important in this approach to show the renormalizability. Conformal sigma models are defined as the fixed point theories of the Wilsonian renormalization group equation. The Wilsonian renormalization group equation with anomalous dimension coincides with the modified Ricci flow equation. The conformal sigma models are characterized by one parameter which corresponds to the anomalous dimension of the scalar fields. Any Einstein-K\"{a}hler manifold corresponds to a conformal field theory when the anomalous dimension is $\gamma=-1/2$. Furthermore, we investigate the properties of target spaces in detail for two dimensional case, and find the target space of the fixed point theory becomes compact or noncompact depending on the value of the anomalous dimension. This is a proceeding to the conference based on the talk given by E.I., Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTeX, 5 eps figures

We construct novel conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use Wilsonian renormalization group equation method to find the fixed points. Existence of fixed points is extremely important in this approach to show the renormalizability. Conformal sigma models are defined as the fixed point theories of the Wilsonian renormalization group equation. The Wilsonian renormalization group equation with anomalous dimension coincides with the modified Ricci flow equation. The conformal sigma models are characterized by one parameter which corresponds to the anomalous dimension of the scalar fields. Any Einstein-K\"{a}hler manifold corresponds to a conformal field theory when the anomalous dimension is $\gamma=-1/2$. Furthermore, we investigate the properties of target spaces in detail for two dimensional case, and find the target space of the fixed point theory becomes compact or noncompact depending on the value of the anomalous dimension., Comment: 20page, 6figures

In this paper, we study three dimensional NL$\sigma$Ms within two kind of nonperturbative methods; WRG and large-N expansion. First, we investigate the renormalizability of some NL$\sigma$Ms using WRG equation. We find that some models have a nontrivial UV fixed point and are renormalizable within nonperturbative method. Second, we study the phase structure of $CP^{N-1}$ and $Q^{N-2}$ models using large-N expansion. These two models have two and three phases respectively. At last, we construct the conformal field theories at the fixed point of the nonperturbative WRG $\beta$ function. This is the review of recently works and is based on the talk of the conference by EI., Comment: To appear in the proceedings of 6th International Conference on Renormalization Group 2005 (RG2005), Helsinki, Finland 30 August - 3 September 2005

Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\cal N}=2$ supersymmetric nonlinear sigma models whose target spaces are Einstein-K\"{a}hler manifolds with positive scalar curvature belongs to this class. hermitian symmetric spaces, being homogeneous, are specially simple examples of these manifolds. To find an independent evidence of the nonperturbative renormalizability of these models, the large N method, another nonperturbative method, is applied to 3-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models on the target spaces $CP^{N-1}=SU(N)/[SU(N-1)\times U(1)]$ and $Q^{N-2}=SO(N)/[SO(N-2)\times SO(2)]$, two typical examples of hermitian symmetric spaces. We find that $\beta$ functions in these models agree with the results of the nonperturbative renormalization group approach in the next-to-leading order of 1/N expansion, and have non-trivial UV fixed points. The $\beta$ function of the $Q^{N-2}$ model receives a nonzero correction in the next-to-leading order of the 1/N expansion. We also investigate the phase structures of our models. The $CP^{N-1}$ model has two phases; SU(N) symmetric and asymmetric phase. The $Q^{N-2}$ model has three phases; Chern-Simons, Higgs and SO(N) broken phases. In the Chern-Simons and Higgs phase, SO(N) symmetry remains unbroken and all dynamical fields becomes massive. An auxiliary gauge field also acquires mass, through an induced Chern-Simons term in the Chern-Simons phase, and through the vacuum expectation value of a di-quark bound state in the Higgs phase., Comment: 24pages, 5figures

On TRIAM-1M, a long duration discharge for more than 5 h was achieved successfully by fully non-inductive lower hybrid current drive. Heat load distribution to the plasma facing components (PFCs) in the 5 h discharge was investigated by using calorimetric measurements. The injected RF power was coincident with the total amount of heat load to PFCs estimated by calorimetric measurement. The power balance including the portion of direct loss power of fast electron, heat flux due to the charge exchange process was able to be estimated in this long duration discharge., Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)

Characteristics of ion acceleration in the internal magnetic reconnection events (IRE) have been studied by means of a neutral particle energy analyzer (NPA) in Tokyo Spherical Tokamak (TST-2). The major and minor radii are 0.38 m and 0.25m, respectively. The magnetic field strength is 0.3T and the maximum plasma current is up to 140 kA. The electron and ion temperatures are 0.4-0.5 keV and 0.1 keV, respectively and the electron density is ~1x1019 m-3. The NPA can be scanned toroidally from q = 74° (cw) to q = 114° (ccw), where q = 90° corresponds to the perpendicular sightline. The direction of the plasma current is cw. The NPA signals are digitized at every 50 ms. The NPA is calibrated in the energy range of 0.1 keV < E < 8.4 keV. When the IRE occurs, it is observed that the plasma current increases by ~ 20% and the loop voltage drops from 0.6 V to-5 V for ~ 0.1 ms. The enhanced charge exchange flux is observed by more than one order of magnitude at ~ 1 keV for this reconnection phase. The ion temperature increases by 80 eV at IREs. The angle q dependence of increment of Ti shows that DTi (q = 74°) is higher than that for q = 114°. This observation suggests that an ion is accelerated initially in the direction of magnetic field lines. The time evolution of the ion distribution function is simulated with a Fokker-Planck code taking into account the electric field effects., Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)

Internal transport barrier (ITB) has been obtained in full lower hybrid current driven (LHCD) plasmas on a superconducting tokamak, TRIMA-1M (R=0.84m, a x b=0.12mx0.18m, BT<8T). The formation of ITB depends on the current density profile, j(r), varied by the power deposition of the lower hybrid (LH). The plasma with ITB can be maintained by the LH power deposited around the foot point of ITB up to 25 sec, which corresponds to more than 100 times of current diffusion time, $\tau$L/R. ITB is terminated by the reduction of current drive efficiency caused by metal impurities accumulation. In some condition, self-organized slow sawtooth oscillations (SSSO) of plasma current, density, temperature, and so on with the period comparable to the current diffusion time have been also observed during ITB discharge. The oscillation has the capability of particle exhaust, as the result, it may play an role in the avoidance of the impurity accumulation and the dilution in the future steady state fusion plasma with ITB, as the edge-localized mode in H-mode., Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)

The three dimensional nonlinear sigma model is unrenormalizable in perturbative method. By using the $\beta$ function in the nonperturbative Wilsonian renormalization group method, we argue that ${\cal N}=2$ supersymmetric nonlinear $\sigma$ models are renormalizable in three dimensions. When the target space is an Einstein-K\"{a}hler manifold with positive scalar curvature, such as C$P^N$ or $Q^N$, there are nontrivial ultraviolet (UV) fixed point, which can be used to define the nontrivial continuum theory. If the target space has a negative scalar curvature, however, the theory has only the infrared Gaussian fixed point, and the sensible continuum theory cannot be defined. We also construct a model which interpolates between the C$P^N$ and $Q^N$ models with two coupling constants. This model has two non-trivial UV fixed points which can be used to define the continuum theory. Finally, we construct a class of conformal field theories with ${\bf SU}(N)$ symmetry, defined at the fixed point of the nonperturbative $\beta$ function. These conformal field theories have a free parameter corresponding to the anomalous dimension of the scalar fields. If we choose a specific value of the parameter, we recover the conformal field theory defined at the UV fixed point of C$P^N$ model and the symmetry is enhanced to ${\bf SU}(N+1)$., Comment: 16 pages, 1 figure, references added

The wave function renormalization constant $Z$, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound $0 \leq Z \leq 1$ in field theories without negative metric states. This unitarity bound implies the positivity of the anomalous dimension of the field in the one-loop approximation. In nonlinear sigma models, however, this bound is apparently broken because of the field dependence of the canonical momentum. The contribution of the bubble diagrams to the anomalous dimension can be negative, while the contributions from more than two particle states satisfies the positivity of the anomalous dimension as expected. We derive the genuine unitarity bound of the wave function renormalization constant., Comment: 8 pages, 2 figures, comments added

The Wilsonian renormalization group (WRG) equation is used to derive a new class of scale invariant field theories with nonvanishing anomalous dimensions in 2-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. When the coordinates of the target manifolds have nontrivial anomalous dimensions, vanishing of the $\beta$ function suggest the existence of novel conformal field theories whose target space is not Ricci flat. We construct such conformal field theories with ${\bf U}(N)$ symmetry. The theory has one free parameter a corresponding to the anomalous dimension of the scalar fields. The new conformal field theories are well behaved for positive a and have the central charge 3N, while they have curvature singularities at the boundary for a<0. When the target space is of complex 1-dimension, we obtain the explicit form of the Lagrangian, which reduces to two different kinds of free field theories in weak and in strong coupling limit. As a consistency test, the anomalous dimensions are reproduced in these two limits. The target space in this case looks like a semi-infinite cigar with one-dimension compactified to a circle., Comment: 14 pages, 3 figures; comments and references added

We propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these manifolds with isometries are explicitly constructed by using the techniques of supersymmetric gauge theories. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes., Comment: LaTeX2e, using espcrc2.sty, 3 pages, no figures, Talk given at the 31st International Conference on High Energy Physics (ICHEP 2002), Amsterdam, The Netherlands, 24-31 July 2002

We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This result is gerenal and does not depend on the specific forms of the K\"{a}hler potentials. We also examine the renormalization group flow in a new model which connects two manifolds with different global symmetries., Comment: LaTeX2e, 20 pages, 3 figures

Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds since they are not holomorphic. Instead, \kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore that they are natural extensions of RNC to the case of \kahler manifolds. The KNC expansion provides a manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models., Comment: LaTeX2e, 24 pages, no figures, the version to appear in Prog. Theor. Phys. 108

We present a simple derivation of the Ricci-flat Kahler metric and its Kahler potential on the canonical line bundle over arbitrary Kahler coset space equipped with the Kahler-Einstein metric., Comment: LaTeX2e, 20 pages, no figures, some minor modification in introduction

We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CP^{N-1}. Imposing an F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle over the complex quadric surface Q^{N-2}. On the other hand, when we promote the U(1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U(M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes., Comment: LaTeX2e, 27 pages, no figures, typos corrected

Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kahler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex line bundles over the Hermitian symmetric spaces. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes., Comment: LaTeX2e, 18 pages, no figures, typos corrected, the version published in NPB