3d large $N$ vector models at the boundary

We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

Development of Caudal Fin Cell Line from Hill Trout Barilius Bendelisis (Hamilton, 1807) for Cytotoxicity and Transfection Studies

A cell line named BBdF-1, established from the caudal fin of hill stream fish Barilius bendelisis, has been subcultured for more than 52 passages and is being maintained in L-15 media containing 20% FBS. Species origin of the cell line was confirmed using amplification of partial region of 16S and COI mitochondrial gene sequences. The optimum temperature for growth of BBdF-1 cell line was found to be 28°C. Karyotyping revealed diploid chromosome number as 50. Cells exhibited strong binding for cytokeratin marker and thus were found to be epithelial-like. Strong green fluorescence was observed in BBdF-1 cells transfected with phrGFP-II-N vector, indicating its suitability for utilization in gene expression and manipulation studies. Successful assessment of cytotoxicity of two heavy metals, viz. mercury and chromium, was performed. The cell line can serve as a useful resource material for early toxicity screening of pesticides/pollutant and gene expression.

Stationary orbits of linear time-varying observation systems

In terms of matrix observability, the necessary and sufficient conditions are obtained for the linear timevarying observation system to have stationary orbits with respect to the linear time-varying transformation group of class C1 . The full invariant of the action of a transformation group is described. It is proved that for any matrix function A c C(T, Rn×n ), there exists such an n-vector function c(t), t c T, that the pair (A, c) is uniformly observable. The algorithm for constructing a stationary system is described.

Self-dualities and renormalization dependence of the phase diagram in 3d O(N) vector models

In the classically unbroken phase, 3d O(N) symmetric ϕ4 vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by κ) and for any N. It is shown that for κ = κ∗ the two fixed points merge and then, for κ < κ∗, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 ϕ4 theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large N in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.