Poles in the SS-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.Comment: 12 pages, minor correction

પ્રાથમિક શિક્ષણ પર જિલ્લા શિક્ષણ અને તાલીમ ભવનોની અસરકારક્તા

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Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter

We present explicit computations and conjectures for $2 \to 2$ scattering matrices in large $N$ {\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.Comment: 66 pages+ 45 pages appendices, 20 figures, Few typos corrected and few references adde

Currents and Radiation from the large DD Black Hole Membrane

It has recently been demonstrated that black hole dynamics in a large number of dimensions $D$ reduces to the dynamics of a codimension one membrane propagating in flat space. In this paper we define a stress tensor and charge current on this membrane and explicitly determine these currents at low orders in the expansion in $\frac{1}{D}$. We demonstrate that dynamical membrane equations of motion derived in earlier work are simply conservation equations for our stress tensor and charge current. Through the paper we focus on solutions of the membrane equations which vary on a time scale of order unity. Even though the charge current and stress tensor are not parametrically small in such solutions, we show that the radiation sourced by the corresponding membrane currents is generically of order $\frac{1}{D^D}$. In this regime it follows that the `near horizon' membrane degrees of freedom are decoupled from asymptotic flat space at every perturbative order in the $\frac{1}{D}$ expansion. We also define an entropy current on the membrane and use the Hawking area theorem to demonstrate that the divergence of the entropy current is point wise non negative. We view this result as a local form of the second law of thermodynamics for membrane motion.Comment: 104 pages plus 69 pages appendix, 1 figure, Minor correction

ENHANCEMENT OF SKIN PERMEABILITY OF ECONAZOLE NITRATE USING NOVEL FLEXISOMAL NANOCARRIERS BY IMPLEMENTING QUALITY BY DESIGN (QBD) APPROACH

Objective: The purpose of this study was an implementation of quality by design (QbD) for the formulation and characterization of econazole nitrate loaded flexisomal nanocarriers (EN-FS) to improve antifungal activity and to enhance skin permeability. Methods: Initially quality target product profile (QTTP) elements were identified and later critical quality attributes (CQA) elements were defined from QTPP elements. Particle size, entrapment efficiency and deformability index were defined as CQAs. Risk assessment was performed by using fishbone diagram and failure mode and effect analysis (FMEA). Design space was created by using fractional factorial design 25-2 as screening design and 32 full factorial design as optimization design to optimize two variables soya phosphatidylcholine concentration(X1) and sodium deoxycholate concentration (X2). Results: Optimized batch of EN-FS was 249.5±3.48 nm, with entrapment efficiency of 88.6±0.89 % and deformability index of 31.75±0.98. Zeta potential analysis showed value of-22.5 mV. Morphological analysis by TEM showed spherical shaped flexisomes, which confirmed the vesicular characteristics. The optimized batch of EN-FS was further made into hydrogels by using sepineo P600 as gelling agent. The % drug diffusion of EN-FS hydrogels had shown 24.68%. With higher skin deposition and higher value of zone of inhibition in antifungal study as compared to plain EN hydrogel. CLSM studies indicated deep penetration of EN-FS in skin layers. Lastly control strategy for EN-FS were developed. Conclusion: It was concluded that EN-FS showed high flexibility and enhanced antifungal activity therefore found to be a potential nanocarriers for drug deposition in skin layers without disturbing skin integrity