Instantons and Non-renormalisation in AdS/CFT

The series of perturbative fluctuations around a multi-instanton contribution to a specific class of correlation functions of supercurrents in $\cal N=4$ supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT correspondence. Subject to certain plausible assumptions, we argue that a given term in the 1/N expansion in such a background receives only a finite number of perturbative corrections in the 't Hooft limit. Such instanton non-renormalisation theorems would explain, for example, the exact agreement of certain weak coupling Yang-Mills instanton calculations with the strong coupling predictions arising from D-instanton effects in string theory amplitudes. These non-renormalisation theorems essentially follow from the assumption of a well defined derivative $(\alpha^{\prime})$ expansion in the string theory dual of the Yang-Mills theory.Comment: 11 pages, harvmac, minor typo correcte

Farming of the seaweed Kappaphycus alvarezii in Tamil Nadu coast - status and constraints

Kappaphycus alvarezii is one of the economically important red algae, which yields carageenan, a commercially important polysaccharide. Carrageenans are used in a variety of commercial applications as gelling, thickening, and stabilizing agents, especially in food products such as frozen desserts, chocolate milk, cottage cheese, whipped cream, instant products, jellies, pet foods and sauces. Besides, carrageenans are used in pharmaceutical formulations, cosmetics and industrial applications such as mining. Commercial cultivation of K. alvarezii originated in Philippines in the year 1960. Since then, countries like Japan, Indonesia, Tanzania, Fiji, Kiripati, Hawaii and South Africa have been cultivating this species on a large scale. In India, cultivation of this seaweed started at Mandapam on the south-east coast of India, during 1995–1997

From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

Entropy Maximization in the Presence of Higher-Curvature Interactions

Within the context of the entropic principle, we consider the entropy of supersymmetric black holes in N=2 supergravity theories in four dimensions with higher-curvature interactions, and we discuss its maximization at points in moduli space at which an excess of hypermultiplets becomes massless. We find that the gravitational coupling function F^(1) enhances the maximization at these points in moduli space. In principle, this enhancement may be modified by the contribution from higher F^(g)-couplings. We show that this is indeed the case for the resolved conifold by resorting to the non-perturbative expression for the topological free energy.Comment: 22 pages, 8 figures, AMS-LaTe

A case study of infestation of Acanthaster pianci in Andaman waters

The starfish feeds on coral polyps and often plague of them are observed on many parts of the Indo – Pacific reefs causing mortality to vast areas of reef corals and their subsequent degradation. The species exhibits a wide range of colour patterns in nature, the common being violet with purplish or blue streaks on the middle of the arms or rusty brown or may be blue. A. planci is widely distributed in the Indo-Pacific from the east coast of East Africa, Red Sea, and then eastward as far as Hawaii. Acanthaster planci was observed at Grub Island, Chester Island, Alexandra Island, Red Skin Island and Twin Islands*.The reefs of Andaman surveyed are dominated by either Acropora spp. or massive Porites in different parts. The maximum concentration of Acanthaster was observed in Grub Island, nearly 50 m away from shore, in shallow waters. The mass mortality of corals observed at sites in the National Marine Park cannot be attributed to predation by Acanthaster. In deeper waters also mass mortality to corals was observed which might be due to many natural causes. Predation by Acanthaster might have played some role in the death of corals but this is not of an alarming state at present

An AdS_3 Dual for Minimal Model CFTs

We propose a duality between the 2d W_N minimal models in the large N 't Hooft limit, and a family of higher spin theories on AdS_3. The 2d CFTs can be described as WZW coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the RG flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS_4 dual for the singlet sector of large N vector models.Comment: 33 pages LaTe

Brane World Dynamics and Adiabatic Matter creation

We have treated the adiabatic matter creation process in various three-brane models by applying thermodynamics of open systems. The matter creation rate is found to affect the evolution of scale factor and energy density of the universe. We find modification at early stages of cosmic dynamics. In GB and RS brane worlds, by chosing appropriate parameters we obtain standard scenario, while the warped DGP model has different Friedmann equations. During later stages, since the matter creation is negligible the evolution reduces to FRW expansion, in RS and GB models.Comment: Replaced with TEX file,No figures, Corrected References and typos. Accepted in IJMP

Economic analysis of farming and wild collection of seaweeds in Ramanathapuram District, Tamil Nadu

The commercially important red alga Kappaphycus alvarezii is widely cultivated along Tamil Nadu coast. Apart from farming, wild collection of seaweed is also being practiced by fishers for their livelihoods. The present study on economics and constraints of farming and wild collection of seaweeds was undertaken in the Ramanathapuram District of Tamil Nadu, employing an expost-facto research design. The study found that the total cost of production for fabricating one bamboo raft (12 x 12 feet) was `1,050/-. The crop duration was 45 days and four to six crops were harvested in a year. The average yield was 200-260 kg per raft per crop. The price of harvested kappaphycus on wet and dry weight basis were `4 and `37.50 per kg respectively. Majority of seaweed farmers earned around `50,000/- to 1,00,000/- annually and the profit margin was 60%. The average gross revenue per trip per group of five members for wild collection of seaweed worked out to `6,700/- and the capital productivity was 0.30. It is interesting to note that about 20% of the respondents were those who left fishing and switched to farming and wild collection of seaweeds

Four-dimensional topological Einstein-Maxwell gravity

The complete on-shell action of topological Einstein-Maxwell gravity in four-dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N=2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.Comment: Published version. Expanded discussion of new results in the introduction and some clarifying remarks added in later sections. 22 pages, uses phyzz