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A bstract We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s , s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function [ 1 ]. Analyticity of the formula in s implies that the scaling dimensions of the defect operators are aligned in Regge trajectories Δ ^ s . These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large s spectrum in the spirit of the work of Alday and Maldacena [ 2 ].

A bstract In this paper we revisit a generalised crossing equation that follows from harmonic analysis on the conformal group, and is of particular interest for the cosmological bootstrap programme. We present an exact solution to this equation, for dimensions two or higher, in terms of 6j symbols of the Euclidean conformal group, and discuss its relevance. In the process we provide a detailed derivation of the analogue of the Biedenharn-Elliot identity for said 6j symbols.

Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the 2-flavour Nambu–Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement transition temperatures in contrast to an enhancement in the chiral transition temperature in its absence. Using standard techniques of finite temperature field theory, the two point thermo-magnetic mesonic correlation functions in the scalar ( σ ) and neutral pseudoscalar ( π 0 ) channels are evaluated to calculate the masses of σ and π 0 considering the AMM of the quarks.

The electrical conductivity of hot and dense quark matter is calculated using the 2-flavour gauged Nambu–Jona–Lasinio (NJL) model in the presence of a chiral imbalance quantified in terms of a chiral chemical potential (CCP). To this end, the in-medium spectral function corresponding to the vector current correlator is evaluated employing the real time formulation of finite temperature field theory. Taking the long wavelength limit of the spectral function we extract the electrical conductivity using the Green–Kubo relation. The thermal widths of the quarks/antiquarks that appear in the expression of electrical conductivity are calculated by considering the 2 → 2 scattering in the NJL model. The scattering amplitudes containing the polarization functions of the mesonic modes in the scalar and pseudoscalar channels are also evaluated by considering finite value of CCP. We find that the ratio of electrical conductivity to temperature has significant dependence on CCP especially in the low temperature region.

A bstract We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

A bstract We define Mellin amplitudes for the fermion-scalar four point function and the fermion four point function. The Mellin amplitude thus defined has multiple components each associated with a tensor structure. In the case of three spacetime dimensions, we explicitly show that each component factorizes on dynamical poles onto components of the Mellin amplitudes for the corresponding three point functions. The novelty here is that for a given exchanged primary, each component of the Mellin amplitude may in general have more than one series of poles. We present a few examples of Mellin amplitudes for tree-level Witten diagrams and tree-level conformal Feynman integrals with fermionic legs, which illustrate the general properties.

Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin, and Yalcin (see Jancovici et al. in J Stat Phys 72(3–4):773–787, 1993, Lebowitz in Phys Rev A 27:1491–1494, 1983, Martin and Yalcin in J Stat Phys 22(4):435–463, 1980), states that the variance of the number of points landing in a set should grow like the surface area instead of the volume unlike i.i.d. random points. In a recent beautiful work (Chatterjee in Rigidity of the three-dimensional hierarchical Coulomb gas, 2017. arXiv preprint. arXiv:1708.01965, To appear in Probability Theory and Related Fields), Chatterjee gave the first proof of such a result in dimension three for a Coulomb type system, known as the hierarchical Coulomb gas, inspired by Dyson’s hierarchical model of the Ising ferromagnet (Dyson in Phys Rev 92:1331–1338, 1953, Dyson in Commun Math Phys 12(2):91–107, 1969). However the case of dimensions greater than three had remained open. In this paper, we establish the correct fluctuation behavior up to logarithmic factors in all dimensions greater than three, for the hierarchical model. Using similar methods, we also prove sharp variance bounds for smooth linear statistics which were unknown in any dimension bigger than two. A key intermediate step is to obtain precise results about the ground states of such models whose behavior can be interpreted as hierarchical analogues of various crystalline conjectures predicted for energy minimizing systems, and could be of independent interest.

The aim of this article is to present the slope stability charts for two layered soil slopes by using the strength reduction method (SRM). The primary focus is to provide a quantitative estimation of the improvement of slope stability when a stronger layer is placed over the weaker layer. The SRM carried in this work comprises a series of finite element lower bound (LB) and upper bound (UB) limit analysis in conjunction with nonlinear optimization. Unlike the limit equilibrium method (LEM), there is no need to consider any prior assumptions regarding the failure surface in SRM. The study is carried out for different combinations of (i) slope angles ( β ), (ii) strength properties of the top and the bottom layer ( c , ϕ ) and (iii) different thickness of the top layer. The failure patterns are shown for a few cases.

Photocatalytic dye degradation is one of the simple and convenient ways to eliminate effluents produced by paper, plastic, printing, and textile industries. ZnS is one of the most investigated catalysts on which different modifications are applied. Here, PVP-assisted zinc sulfide (ZnS) nanopowder is prepared hydrothermally. The photoluminescence spectra signify the generated intermediate state which is attributed to sulfur (S) vacancy as obtained from the theoretical analysis. This defect-induced ZnS has shown excellent Rhodamine B (RhB) dye degradation of 95% in 100 min with dye sensitization effect under UV irradiation. Under visible light, the degradation of RhB is only 50% in the presence of ZnS. The sensitization of RhB in the presence of UV light signifies the generation of visible light through the intermediate states caused by S vacancy. However, to eliminate the disadvantage of photocatalysis in highly concentrated wastewater management and expense of UV source, RhB is degraded by sonocatalysis, and 70% of dye is removed within 100 min in the presence of ZnS nanopowder. Therefore, the efficient catalytic dye degradations are achieved employing the minimum amount of ZnS powder.

Rheumatoid arthritis (RA) is a chronic inflammatory disease associated with subsequent damage to the bone joints with a global incidence rate of 0.5–1%. To combat with RA various commercially available anti-inflammatory drugs like non-steroidal anti-inflammatory drugs (NSAIDs) are commonly practiced; however, their long-term exposure often results in eliciting gastrointestinal and renal toxicity. Given this, the scientific communities are searching for an alternative therapeutic option that seems less injurious and equally efficacious. Equisetum diffusum D. Don, from the Equisetaceae family, is a native pteridophyte species of the sub-Himalayan region of India and has been reported to have a diverse array of pharmacological properties. The decoction and macerated whole plant extract has been used by various tribal communities (like Tagin, Galo, Adi, Kukis, Meiteis, Mulam) throughout the tropical and sub-tropical Asian countries for the treatment of arthritis, bone fractures, back pain, and abrasives. The present research is focused on determining the anti-arthritic potential of E. diffusum whole plant methanol extract (EDME) in adjuvant-induced arthritic rats. Oral administration with 250 and 500 mg/kg b.w. doses of EDME significantly restored paw-edema, arthritic scoring, and normal body weight. EDME treatment also normalized the haematological, biochemical, radiological, and histological status when compared to the arthritic control rats. The methanol extract significantly ( p  < 0.05) attenuated arthritis progression by downregulating the gene expression of pro-inflammatory mediators, like COX-2, TNF-α, IL-6, and upregulating the expression of anti-inflammatory mediators PPAR-γ, Iκβ in the blood, in a dose-dependent manner. Significantly, EDME also reduced the serum concentration of COX-2, TNF-α, and IL-6 compared to arthritic control rats ( p  < 0.05). The treatment with EDME also normalized the oxidative stress level in liver by restoring the GSH level, CAT and SOD activities and reducing the elevated MDA level. HPTLC and LC–MS/MS analyses of EDME confirmed the presence of potent polyphenols (chlorogenic acid, 4-hydroxycinnamic acid) and flavonoids (kaempferol), thereby suggesting the anti-arthritic property of the plant. All our findings established the anti-arthritic potential of E. diffusum extract in chronic arthritis model on a strong ground.