Note on gauge and gravitational anomalies of discrete ZNZ_N symmetries

In this note, we discuss the consistency conditions which a discrete $Z_N$ symmetry should satisfy in order that it is not violated by gauge and gravitational instantons. As examples, we enlist all the $Z_N$ ${\cal R}$-symmetries as well as non-${\cal R}$ $Z_N$ symmetries (N=2,3,4) in the minimally supersymmetric standard model (MSSM) that are free from gauge and gravitational anomalies. We show that there exists non-anomalous discrete symmetries that forbid Baryon number violation up to dimension 6 level (in superspace). We also observe that there exists no non-anomalous $Z_3$ ${\cal R}$-symmetry in the MSSM. Furthermore, we point out that in a theory with one Majorana spin 3/2 gravitino, a large class of $Z_4$ ${\cal R}$-symmetries are violated in the presence of Eguchi-Hanson (EH) gravitational instanton. This is also in general true for higher $Z_N$ ${\cal R}$-symmetries. We also notice that in 4 dimensional ${\cal N}=1$ supergravity, the global $U(1)$ ${\cal R}$-symmetry is always violated by the EH instanton irrespective of the matter content of the theory.Comment: Version to appear in JHE

On monopole operators in supersymmetric Chern-Simons-matter theories

We discuss monopole operators in $U(N_c)$ Chern-Simons-matter theories in three space-time dimensions. We mention an apparent problem in the matching of such operators in dualities between non-supersymmetric theories, and suggest a possible resolution. A similar apparent problem exists in the mapping of chiral monopole operators in theories with ${\cal N}=2$ supersymmetry. We show that in many theories the lowest naive chiral monopole operator is actually not chiral, and we find the lowest monopole operator that is actually chiral in these theories. It turns out that there are several different forms of this operator, depending on the number of colors, the number of flavours, and the Chern-Simons level. Since we use the supersymmetric index to find the lowest chiral monopoles, our results for these monopoles are guaranteed to be invariant under the dualities in supersymmetric theories. The theories we discuss are believed to be dual in the 't~Hooft large $N_c$ limit to classical high-spin gravity theories. We argue that these theories (supersymmetric or not) should not have classical solutions charged under the $U(1)$ gauge field in the high-spin multiplet.Comment: 39 pages. v2: fixed typo

Superspace formulation and correlation functions of 3d superconformal field theories

We study $3d$ SCFTs in the superspace formalism and discuss superfields and on-shell higher spin current multiplets in free $3d$ SCFTs with $\mathcal{N}= 1,2,3,4$ and $6$ superconformal symmetry. For $\mathcal{N}=1$ 3d SCFTs we determine the superconformal invariants in superspace needed for constructing 3-point functions of higher spin operators, find the non-linear relations between the invariants and consequently write down all the independent invariant structures, both parity even and odd, for various 3-point functions of higher spin operators.Comment: typos corrected, references added. Accepted for publication in JHE

Decoding X-ray observations from centres of galaxy clusters using MCMC

We correct for the use of electron densities instead of total gas density in the pressure fits which were used to derive the local free-fall times (t$_{\rm ff}$) in the original paper

AYURVEDA: EMERGING BENEFACTION TO PUBLIC HEALTH CARE

The social impact of ill health is on the rise, with some diseases affecting not only the health of individuals but also that of a nations economy with their increasing healthcare costs. The enormous complexity of human body offers scope to conceptualize its dynamic organization in a number of ways such as structural, biochemical, functional, etc. The conventional western medicine views the body from a structural perspective, whereas Ayurveda, the ancient medical system of India, understands the human body from the perspective of functions/Tridoshas (Vata, Pitta and Kapha). Ayurveda is a holistic science and Ayurvedic treatment aims not only at removal of disease, but also at the restoration of the equilibrium of bodily functions. These different viewpoints of Ayurveda and western medicine have resulted not only in the use of different terminologies and metaphors to explain the human system but also in their different approaches to health and illness. In the recent past there has been a growing interest in Ayurvedic system of Medicine and their relevance to public health. In this context, there is a critical need to mainstream Ayurveda into public health care to achieve the objective of improved access to healthcare facilities

Sectorial Trends Patterns and Prospects of Auto Component Industry in India

The paper highlights the growth of Indian Automobile Industry, particularly to the Indian Auto Component Industry relating with Investments and Foreign Direct Investment in the equity inflows, drawing comparison with the developments and growth of Automobile Industry domestically and globally. The growth of Indian Auto Component Industry in the first decade of the twenty first century is phenomenal. The Industry transformed gradually in stages from serving just Indian market, majority to replacement market, to global OEMs and replacement market. Now, the Auto Component Manufacturers Association (ACMA) has significance for global recognition and has a positive impact on GDP. It has played a vital role in the growth of Indian Automobile sector in last few years and in future as per Automotive Plan 2006-16, and Automotive sector five year plan 2012–17, as projected by Department of Heavy Industry.  The  growth  of  this  sub  sector  has  a  pivotal role  in  the developments and growth of Indian Automobile Industry and economy rather it is dependent on Automobile Industry growth, locally and worldwide. Keywords: OEMs, ACMA, ACT

Metformin induced yellow nails: a rare entity

This article reports an interesting and a rare case of metformin induced nail disorder in a middle aged female with type 2 diabetes. The patient had been receiving metformin one 1500mg daily from the last 6 months and noticed her finger nails gradually thickened and turned yellow. On stopping the metformin, the nails gradually normalized. The patient was treated further with glimepiride and insulin glargine. After 3 months of discontinuation of metformin there was a significant improvement in the nails. Clinicians should be aware of metformin induced yellow discolouration of nails, though a curable and reversible condition if diagnosed well in time