Charged structure constants from modularity

We derive a universal formula for the average heavy-heavy-light structure constants for 2d CFTs with non-vanishing u(1) charge. The derivation utilizes the modular properties of one-point functions on the torus. Refinements in N=2 SCFTs, show that the resulting Cardy-like formula for the structure constants has precisely the same shifts in the central charge as that of the thermodynamic entropy found earlier. This analysis generalizes the recent results by Kraus and Maloney for CFTs with an additional global u(1) symmetry. Our results at large central charge are also shown to match with computations from the holographic dual, which suggest that the averaged CFT three-point coefficient also serves as an useful probe of detecting black hole hair.Comment: 22 pages, 1 figure; v2: approximates published versio

Modular crossings, OPE coefficients and black holes

In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the pillow geometry and thereby crossing symmetry gets translated into a modular property. We use these modular features to derive a universal asymptotic formula for OPE coefficients in which one of the operators is averaged over heavy primaries. The coarse-grained heavy channel then reproduces features of the gravitational 2-to-2 S-matrix which has black holes as their intermediate states.Comment: 6 pages and a pillow; v3 : approximates published versio

Monstrous entanglement

The Monster CFT plays an important role in moonshine and is also conjectured to be the holographic dual to pure gravity in AdS3. We investigate the entanglement and Renyi entropies of this theory along with other extremal CFTs. The Renyi entropies of a single interval on the torus are evaluated using the short interval expansion. Each order in the expansion contains closed form expressions of the modular parameter. The leading terms in the q-series are shown to precisely agree with the universal corrections to Renyi entropies at low temperatures. Furthermore, these results are shown to match with bulk computations of Renyi entropy using the one-loop partition function on handlebodies. We also explore some features of Renyi entropies of two intervals on the plane.Comment: 41 pages, 4 figures; v2: typos corrected, approximates published versio

Probing thermality beyond the diagonal

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE coefficients via the modular bootstrap is performed to extract the behaviour of the off-diagonal matrix elements. We also probe this sector using semi-classical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirms the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.Comment: 27 pages, 2 figure

Formulation and in vitro study of Ibuprofen loaded crosslinked sodium alginate and gellan gum microspheres

Ibuprofen loaded microspheres were prepared using sodium alginate and gellan gum and were cross-linked by maleic anhydride, aluminium chloride. The resulting microspheres were evaluated by in-vitro release study, swelling index, microscopic analysis and entrapment efficiency. DSC study shows there was no interaction between drug and excipients. Entrapment was found good in all the formulations while the maximum entrapment (97.6%) was recorded in formulation cross-linked by aluminium chloride and their average particle size were 150 to 160 m. Approximately 50% of drug was released by the formulation cross-linked by aluminium chloride (F2) over a period of 6 hours. From this experiment, it is observed that the formulation with cross-linked by aluminium chloride is the better formulation among others due to good release profile and entrapment efficiency

Virasoro blocks and quasimodular forms

We analyse Virasoro conformal blocks in the regime of heavy intermediate exchange $(h_p \rightarrow \infty)$. For the 1-point block on the torus and the 4-point block on the sphere, we show that each order in the large-$h_p$ expansion can be written in closed form as polynomials in the Eisenstein series. The appearance of this structure is explained using the fusion kernel and, more markedly, by invoking the modular anomaly equations via the 2d/4d correspondence. We observe that the existence of these constraints allows us to develop a faster algorithm to recursively construct the blocks in this regime. We then apply our results to find corrections to averaged heavy-heavy-light OPE coefficients.Comment: 35 pages, 2 figure

Migration in the Indian Bengal Delta and the Mahanadi Delta `a review of the literature

This series is based on the work of the Deltas, Vulnerability and Climate Change: Migration and Adaptation (DECCMA) project, funded by Canada’s International Development Research Centre (IDRC) and the UK’s Department for International Development (DFID) through the Collaborative Adaptation Research Initiative in Africa and Asia (CARIAA).Like anywhere else in India, Migration over past several decades from ISD have occurred for better livelihood opportunities and earning better income, acquiring higher education or skills.Such migration can be seen as seasonal in nature (CRS, 2010; CSE, 2012). But over the years, studies in Indian Bengal Delta are largely concentrating on migration resulting from natural disasters like cyclones, storm surges, erosion of land, breaching of embankments or submergence of islands. (Hazra Sugata et.al., 2002; CRS, 2010; CSE, 2012; Bera M., 2013; Ghosh A.K., 2014; GhoshTuhin, et.al., 2014; Mukherjee, 2014

Linking IPCC AR4 & AR5 frameworks for assessing vulnerability and risk to climate change in the Indian Bengal Delta

The International Panel on Climate Change (IPCC) AR5 (Fifth Assessment Report, 2014) conceptual approach and terminology is aligned with a concept of risk which differs from the previous framework (AR4). This study draws links between the AR5 concept of risk with the previous concept of vulnerability (AR4). The most significant difference between the results of the AR4 and AR5 approaches is the change in sub-district level relative rankings. Findings show that Basanti, in the Bengal Delta, is the most vulnerable sub-district using the AR4 approach, whereas Gosaba is found to be highly exposed to risk using the AR5 approach.UK Government's Department for International Development (DFID