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In the context of holographic conformal field theories (CFTs), a system of linear partial differential equations was recently proposed to be the higher-dimensional analog of the null-state equations in $d=2$ CFTs at large central charge. Solving these equations in a near-lightcone expansion yields solutions that match the minimal-twist multi-stress tensor contributions to a heavy-light four-point correlator (or a thermal two-point correlator) computed using holography, the conformal bootstrap, and other methods. This note explores the exact solutions to these equations. We begin by observing that, in an expansion in terms of the ratio between the heavy operator's dimension and the central charge, the $d=2$ correlator involving the level-two degenerate scalars at each order can be represented as a Bessel function; the resummation yields the Virasoro vacuum block. We next observe a relation between the $d=2$ correlator and the $d=4$ near-lightcone correlator involving light scalars with the same conformal dimension. The resummed $d=4$ correlator takes a simple form in the complex frequency domain. Unlike the Virasoro vacuum block, the resummation in $d=4$ leads to essential singularities. Similar expressions are also obtained when the light scalar's dimension takes other finite values. These CFT results correspond to a holographic computation with a spherical black hole. In addition, using the differential equations, we demonstrate that the correlators can be reconstructed via certain modes. In $d=2$, these modes are related to the Virasoro algebra., Comment: 39 pages, v2: notation improved

In two-dimensional CFTs with a large central charge, the level-two BPZ equation governs the heavy-light scalar four-point correlator when the light probe scalar has dimension $h= - {1\over 2}$; the corresponding linear ordinary differential equation can be recast into a schematic form $x^2 u_{xx}+u=0$. In this paper, we make an observation that in a class of four-dimensional CFTs with a large central charge, the heavy-light scalar correlator in the near-lightcone limit obeys a similar equation, $x^3 u_{xxxy}+u=0$, when the light scalar has dimension $\Delta=-1$. We focus on the multi-stress tensor sector of the theory and also discuss the corresponding equations for the cases with $\Delta = -2, -3$. The solutions to these linear partial differential equations in higher dimensions are shown, after a suitable change of variables, to reproduce the near-lightcone correlators previously obtained via holography and the conformal bootstrap., Comment: 27 pages, v2: minor corrections and references added, v3: notation improved

We consider thermal stress-tensor two-point functions in holographic theories in the near-lightcone regime and analyse them using the operator product expansion (OPE). In the limit we consider only the leading-twist multi-stress tensors contribute and the correlators depend on a particular combination of lightcone momenta. We argue that such correlators are described by three universal functions, which can be holographically computed in Einstein gravity; higher-derivative terms in the gravitational Lagrangian enter the arguments of these functions via the cubic stress-tensor couplings and the thermal stress-tensor expectation value in the dual CFT. We compute the retarded correlators and observe that in addition to the perturbative OPE, which contributes to the real part, there is a non-perturbative contribution to the imaginary part., Comment: 37 pages. v2: minor changes

Averaged Null Energy Conditions (ANECs) hold in unitary quantum field theories. In conformal field theories, ANECs in states created by the application of the stress tensor to the vacuum lead to three constraints on the stress-tensor three-point couplings, depending on the choice of polarization. The same constraints follow from considering two-point functions of the stress tensor in a thermal state and focusing on the contribution of the stress tensor in the operator product expansion (OPE). One can observe this in holographic Gauss-Bonnet gravity, where ANEC saturation coincides with the appearance of superluminal signal propagation in thermal states. We show that, when this happens, the corresponding generalizations of ANECs for higher-spin multi-stress tensor operators with minimal twist are saturated as well and all contributions from such operators to the thermal two-point functions vanish in the lightcone limit. This leads to a special near-lightcone behavior of the thermal stress-tensor correlators -- they take the vacuum form, independent of temperature., Comment: 38 pages. v3: Minor changes, references added

Photoelectrocatalytic (PEC) reduction of N2 to ammonia (NH3) is emerging as the potential alternative to overcome the standard Haber-Bosch approach. In this communication, solar N2 reduction was demonstrated with molybdenum carbide (Mo2C) co-catalyst assisted indium gallium nitride (InGaN) nanowires. The effect of aiding Mo2C on InGaN NWs arrests the dark current and demonstrated the saturation current under illumination was briefly elucidated. Large NH3 production of 7.2 gh-1cm-2 with high Faradaic efficiency of 12.6 % was realized at -0.2 V vs. reversible hydrogen electrode for the Mo2C/GaN/InGaN heterostructure. Notably, the proposed heterostructure also exemplifies excellent stability and reproducibility with excellent selectivity in the long-term chronoamperometry analysis. Further, the incorporation of GaN buffer layer in between Mo2C and InGaN NWs was deeply investigated. From Density Functional Theory (DFT) analysis, the incorporation of GaN buffer layer aids the suitable band edge position for the transfer of photogenerated charge carrier from InGaN to Mo2C co-catalyst, and unique 3d orbital of Mo2C is highly suitable to hold N2 for effective reduction to NH3.

By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in $d=4$ conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor $T^{++}$ on a $d=2$ plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the $T^{--}$ component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of $d=4$ scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/${\cal W}$-algebra vacuum block-like structure., Comment: 16 pages