Classification of N=2 supersymmetric CFT_{4}s: Indefinite Series

Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s. Since the geometric engineering of these CFT$_{4}$s involve type II strings on K3 fibered CY3 singularities, we conjecture the existence of three kinds of singular complex surfaces containing, in addition to the two standard classes, a third indefinite set. To illustrate this hypothesis, we give explicit examples of K3 surfaces with H$_{3}^{4}$ and E$_{10}$ hyperbolic singularities. We also derive a hierarchy of indefinite complex algebraic geometries based on affine $A_{r}$ and T$$ algebras going beyond the hyperbolic subset. Such hierarchical surfaces have a remarkable signature that is manifested by the presence of poles.Comment: 12 pages, 2 figure

Processing And Pelletizing Of Low Grade Malaysian Iron Ore.

Kajian telah dilakukan ke atas bijih besi bergred rendah yang diperoleh daripada KSG Resources (M) Sdn. Bhd. Sungai Temau, Pahang, Malaysia. Low grade iron ore obtained from KSG Resources (M) Sdn. Bhd., Sungai Temau, Pahang, Malaysia, have been studied

On Thermodynamics of AdS Black Holes in M-Theory

Motivated by a recent work on asymptotically AdS_4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2 and M5-branes. Concretely, we consider AdS black holes in AdS_{p+2}\times S^{11-p-2}, where p=2,5 by interpreting the number of M2 (and M5-branes) as a thermodynamical variable. We study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then, we compute the thermodynamical curvatures from the Quevedo metric for M2 and M5-branes geometries to reconsider the stability of such black objects. The Quevedo metric singularities recover similar stability results provided by the phase transition program.Comment: 16 pages, 12 figures. Late

Ehrenfest Scheme of Higher Dimensional Topological AdS Black Holes in The Third Order Lovelock-Born-Infeld Gravity

Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in Lovelock-Born-Infeld gravity. In particular, we give an explicit expression of the universal number \chi=\frac{P_c v_c}{T_c} in terms of the space dimension $n$. Then, we examine the phase transitions at the critical points of such topological black holes for 6 \leq n \leq 11 as required by the physical condition of the thermodynamical quantities. More precisely, the Ehrenfest equations have been checked revealing that the black hole system undergoes a second phase transition at the critical points.Comment: 18 pages, latex with 10 figures, titled modified, section added, typos corrected, accepted for publication in International Journal of Geometric Methods in Modern Physics (2015