A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry

In this letter, we elaborate on the SL(2,Z) action on three dimensional conformal field theories with U(1) symmetry introduced by Witten, by trying to give an explicit verification of the claim regarding holographic dual of the S operation in AdS/CFT correspondence. A consistency check with the recently proposed prescription on boundary condition of bulk fields when we deform the boundary CFT in a non-standard manner is also discussed.Comment: LaTex, 1+15 pages, 1 figure, v2: discussion in terms of deformation theory is adde

Analytical hierarchy approach for load shedding scheme: a case study based on the Johor System

In general, the highly development environment in the society or the natural interruptions can cause loss of the power supply due to the burden of the generator. In industries, this can cause million of losses when the shortage of supply occurs. Usually, the supply will be back-upped in the storage system. If the over demand is uncontrolled, or when there is no decision-making in removing a certain load, there will be a trouble in the power system. Certain loads will be removed depending on some importance or criteria such as operating load and area power. This requires some decision-making in order order to choose the best load(s) to be cut off. In order to do that, Multi Criteria Decision Making (MCDM) can be applied in determination of the load shedding scheme in the electric power system. The objective of this thesis is to justify a load shedding scheme for an islanded power system. This thesis proposes methodologies for load shedding scheme for the islanded electric power system by using Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (Fuzzy AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In this thesis, the load shedding scheme is applied to several systems such as large pulp mill electrical system, IEEE 118 bus test case system, Selangor electrical system and Johore electrical system. Models are built up on the base of analysing correlative factors with examples given to indicate how the AHP, Fuzzy AHP and TOPSIS are applied. From this thesis, a series of analyses are conducted and the results are determined. Analyses are made, and the results have shown that AHP, Fuzzy AHP and TOPSIS can be used in determination of the load shedding scheme in pulp mill system, IEEE 118 bus system, Selangor system and Johore system. Among these three MCDM methods, the results shown by TOPSIS is the most effective solution because of the effectiveness of load shedding is the highest

Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics

We provide a resolution of an old issue in weak coupling computation of the Chiral Magnetic Effect (CME) current, where a free chiral fermion theory gives two different results depending on the order of the two limits, $\omega\rightarrow 0$ (frequency) and $k\rightarrow 0$ (spatial momentum). We first argue based on hydrodynamics that in any reasonable interacting theory of chiral fermions the non-commutativity between the two limits should be absent, and we demonstrate this at weak coupling regime in two different frameworks: kinetic theory in the relaxation time approximation, and diagrammatic computation with resummation of damping rate. In the latter computation, we also show that the "pinch" singularity, which would make the summation of ladder diagrams necessary as in the P-even correlation function, is absent in the relevant P-odd correlation function. The correct value of CME current is reproduced even in the presence of relaxation dynamics in both computations.Comment: 26 pages, 3 figure

Second Order Transport Coefficient from Chiral Anomaly at Weak Coupling: Diagrammatic Resummation

We compute one of the second order transport coefficients arising from the chiral anomaly in a high temperature weakly coupled regime of quark-gluon plasma. This transport coefficient is responsible for the CP-odd current that is proportional to the time derivative of the magnetic field, and can be considered as a first correction to the chiral magnetic conductivity at finite, small frequency. We observe that this transport coefficient has a non-analytic dependence on the coupling as $\sim 1/(g^4 \log(1/g))$ at weak coupling regime, which necessitates a re-summation of infinite ladder diagrams with leading pinch singularities to get a correct leading log result: a feature quite similar to that one finds in the computation of electric conductivity. We formulate and solve the relevant CP-odd Schwinger-Dyson equation in real-time perturbation theory that reduces to a coupled set of second order differential equations at leading log order. Our result for this second order transport coefficient indicates that chiral magnetic current has some resistance to the time change of magnetic field, which may be called "chiral induction effect". We also discuss the case of color current induced by color magnetic field.Comment: 54 pages, 8 figure