Constraints on parity violating conformal field theories in d=3d=3

We derive constraints on three-point functions involving the stress tensor, $T$, and a conserved $U(1)$ current, $j$, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures for the $\langle T T T \rangle$ and $\langle j j T \rangle$ correlation functions which are unique to three space-time dimensions. Let the parameters which determine the $\langle T T T \rangle$ correlation function be $t_4$ and $\alpha_T$ , where $\alpha_T$ is the parity-violating contribution. Similarly let the parameters which determine $\langle j j T \rangle$ correlation function be $a_2$, and $\alpha_J$ , where $\alpha_J$ is the parity-violating contribution. We show that the parameters $(t_4, \alpha_T)$ and $(a_2, \alpha_J)$ are bounded to lie inside a disc at the origin of the $t_4$ - $\alpha_T$ plane and the $a_2$ - $\alpha_J$ plane respectively. We then show that large $N$ Chern-Simons theories coupled to a fundamental fermion/boson lie on the circle which bounds these discs. The `t Hooft coupling determines the location of these theories on the boundary circles.Comment: Minor typos corrected, Figures changed , References adde

Bootstrap and collider physics of parity violating conformal field theories in d=3d=3

We study the crossing equations in $d=3$ for the four point function of two $U(1)$ currents and two scalars including the presence of a parity violating term for the $s$-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the $t$-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd $s$-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order in light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.Comment: References update

Spectral sum rules for conformal field theories in arbitrary dimensions

We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. The sum rules result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Hofman-Maldacena variables $t_2, t_4$ which determine the three point function of the stress tensor. For theories which admit a two derivative gravity dual this proportionality constant is given by $\frac{d}{2(d+1)}$. We then use causality constraints and obtain bounds on the sum rule which are valid in any conformal field theory. Finally we demonstrate that the high frequency behaviour of the spectral function in the vector and the tensor channel are also determined by the Hofman-Maldacena variables.Comment: Corrected typos, JHEP versio

Management of Rangelands and Forests for Sustainable Mithun Farming by Chakhesang Tribe of Nagaland

Mithun (Bos frontalis) belonging to the family Bovidae is a unique bovine mainly found in the North-Eastern hilly region of India and neighbouring countries (Dhali et al., 2009). The animal has an important place in the socio-economic life of the tribal communities and primarily reared as sacrificial animal during religio-cultural ceremonies. Feeding habits of Mithun differs from their domestic counterparts cattle; like they prefer browsing as compared to the grazing behaviour of the later. Mithun forage on forest grasses, shrubs and tree leaves available in the jungle and they nibble them like goats (Gupta et al., 1996). As mithun prefers browsing, so they are reared in demarcated forests and rangelands under natural conditions by the tribal communities and during the course of rearing, these communities manage both, the mithun and forest ranges. Land owning pattern in Nagaland is different and most of the land is owned by the community that gives right to use and manage the resources to mithun owners. Forest departments owns certain category of forests classified as Reserved forest, Protected forests, Wildlife sanctuaries, National Parks and Botanical gardens that comprises of about 16.7% of the total available forest area. Remaining around 83.3% of forests are owned by the villagers and Government has no control over these (Singh et al., 2009). Since the Government has very limited role, so management practices largely varies with the communities residing there. Communities have their own way of exploiting resources and to replenish them and that differs with the communities. The farmers who owns mithun has more proximity with forests and rangelands so management practices adopted by them is being presented in this paper

Differential Neutrino Rates and Emissivities from the Plasma Process in Astrophysical Systems

The differential rates and emissivities of neutrino pairs from an equilibrium plasma are calculated for the wide range of density and temperature encountered in astrophysical systems. New analytical expressions are derived for the differential emissivities which yield total emissivities in full agreement with those previously calculated. The photon and plasmon pair production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are provided. The appropriate Legendre coefficients of these kernels, in forms suitable for multi-group flux-limited diffusion schemes are also computed.Comment: 27 pages and 10 figures. Submitted to Phys. Rev.

The photo-neutrino process in astrophysical systems

Explicit expressions for the differential and total rates and emissivities of neutrino pairs from the photo-neutrino process $e^\pm + \gamma \to e^\pm + \nu + \bar\nu$ in hot and dense matter are derived. Full information about the emitted neutrinos is retained by evaluating the squared matrix elements for this process which was hitherto bypassed through the use of Lenard's identity in obtaining the total neutrino emissivities. Accurate numerical results are presented for widely varying conditions of temperature and density. Analytical results helpful in understanding the qualitative behaviors of the rates and emissivities in limiting situations are derived. The corresponding production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are developed. The appropriate Legendre coefficients of these kernels, in forms suitable for multigroup flux-limited diffusion schemes are also provided.Comment: 26 pages and 7 figures. Version as accepted in Phys. Rev. D; three figures and related discussion revise

Closing the Gap between ‘Expert’ and ‘Lay’ Knowledge in the Governance of Wastewater: Lessons and Reflections from New Delhi

The wastewater crisis in megacities of the Global South is increasingly recognised. However, sector?driven approaches (of river pollution, sewerage, or city?wide drainage) have had limited success in tackling this multifaceted problem. This article seeks to dynamise debates by positioning the current crisis in relation to contests of knowledge. Focusing on wastewater governance in Delhi, the article explores the question which different knowledges about wastewater exist in scientific communities, governments, and amongst citizens. What is frequently understood as ‘expert’ knowledge of the Central Pollution Control Board, is juxtaposed with the ‘lay’ experiences of citizens residing in one unauthorised colony in East Delhi. Exploring both, the article provides insights on the mechanisms through which community experiences are excluded from policy deliberations, leading to major wastewater?related problems being overlooked. The article then calls for enhanced attention to knowledge integration, thus strengthening the participation of citizens in formulation and implementation of wastewater programmes