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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

We study the $TT$ OPE in $d>2$ CFTs whose bulk dual is Einstein gravity. Directly from the $TT$ OPE, we obtain, in a certain null-like limit, an algebraic structure consistent with the Jacobi identity: $[{\cal L}_m, {\cal L}_n]= (m-n) {\cal L}_{m+n}+ C m (m^2-1) \delta_{m+n,0}$. The dimensionless constant $C$ is proportional to the central charge $C_T$. Transverse integrals in the definition of ${\cal L}_m$ play a crucial role. We comment on the corresponding limiting procedure and point out a curiosity related to the central term. A connection between the $d>2$ near-lightcone stress-tensor conformal block and the $d=2$ $\cal W$-algebra is observed. This note is motivated by the search for a field-theoretic derivation of $d>2$ correlators in strong coupling critical phenomena., Comment: 15 pages

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge $C_T$, we clarify the properties of stress tensor composite primary operators of minimal twist, $[T^m]$, using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\langle \mathcal{O}_L\mathcal{O}_L [T^m]\rangle$, where $\mathcal{O}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $\langle TT \mathcal{O}_L\rangle$, the three-point coupling $\langle \mathcal{O}_L\mathcal{O}_L [T^2]\rangle$ is modified at large $C_T$ if $\langle TT\mathcal{O}_L \rangle \sim \sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to $\mathcal{O}_L$ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-$\ell \geq 2$ bulk field at tree level, or any spin $\ell$ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively., Comment: 25+10 pages

We consider two $d \geq 2$ conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we compute the heat kernel coefficients and interface central charges in free theories. The results are consistent with the known boundary CFT data via the folding trick. In $d=4$, two interface invariants generally allowed as anomalies turn out to have vanishing interface charges. These missing invariants are constructed from components with odd parity with respect to flipping the orientation of the defect. We conjecture that all invariants constructed from components with odd parity may have vanishing coefficient for symmetric interfaces, even in the case of interacting interface CFT., Comment: 14 pp; v2: clarifications added, introduction expanded

Motivated by developing a field-theoretic algebraic approach to the universal part of the stress-tensor sector of a scalar four-point function in a class of higher-dimensional CFTs, we construct a mode operator, ${\cal L}_m$, near the lightcone in $d=4$ CFTs and show that it leads to a Virasoro-like commutator, including a regularized central-term. As an example, we describe how to reproduce the $d=4$ single-stress tensor exchange contribution in the lightcone limit by a mode summation. A general-$d$ extension is included. We comment on possible generalizations., Comment: 13 pp; v2: various improvements, general-d stress-tensor exchange added. v3: minor corrections, published version

Gravitational shockwaves are insensitive to higher-curvature corrections in the action. Recent work found that the OPE coefficients of lowest-twist multi-stress-tensor operators, computed holographically in a planar black hole background, are insensitive as well. In this paper, we analyze the relation between these two limits. We explicitly evaluate the two-point function on a shockwave background to all orders in a large central charge expansion. In the geodesic limit, we find that the ANEC exponentiates in the multi-stress-tensor sector. To compare with the black hole limit, we obtain a recursion relation for the lowest-twist products of two stress tensors in a spherical black hole background, letting us efficiently compute their OPE coefficients and prove their insensitivity to higher curvature terms. After resumming the lowest-twist stress-tensors and analytically continuing their contributions to the Regge limit, we find a perfect agreement with the shockwave computation. We also discuss the role of double-trace operators, global degenerate states, and multi-stress-tensor conformal blocks. These holographic results suggest the existence of a larger universal structure in higher-dimensional CFTs., Comment: 28+6 pages, 2 figures; v2: typos corrected, refs added

Starting with the general stress-tensor commutation relations consistent with the Poincar\'e algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in $d>2$ conformal field theories., Comment: 5 pp. V2: minor corrections, reference added

We probe the conformal block structure of a scalar four-point function in $d\geq2$ conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge $C_T$. Neither supersymmetry nor unitary is assumed. Higher-twist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limit in this paper, we include some preliminary analysis of the spherical black hole case in an appendix., Comment: 63 pp; v2: comments on additional bulk interactions added

In the context of boundary conformal field theory, we investigate whether the boundary trace anomaly can depend on marginal directions in the presence of supersymmetry. Recently, it was found that a graphene-like non-supersymmetric conformal field theory with a four-dimensional bulk photon and a three-dimensional boundary electron has two boundary central charges that depend on an exactly marginal direction, namely the gauge coupling. In this work, we supersymmetrize this theory, paying special attention to the boundary terms required by supersymmetry. We study models with 4, 8, and 16 Poincar\'e supercharges in the bulk, half of which are broken by the boundary. In all cases, we find that at all orders in perturbation theory, the gauge coupling is not renormalized, providing strong evidence that these theories are boundary conformal field theories. Moreover, the boundary central charges depend on the coupling. One possible exception to this dependence on marginal directions is that the difference between the two charges is coupling independent at one-loop in the maximally supersymmetric case. In our analysis, a possible boundary Chern-Simons term is incorporated by a bulk $\theta$-term., Comment: 47 pages; v2: footnotes and references added

We study a 6d model of a set of self-dual 2-form $B$-fields interacting with a non-abelian vector $A$-field which is restricted to a 5d subspace. One motivation is that if the gauge vector could be expressed in terms of the $B$-field or integrated out, this model could lead to an interacting theory of $B$-fields only. Treating the 5d gauge vector as a background field, we compute the divergent part of the corresponding one-loop effective action which has the $(DF)^2+F^3$ structure and compare it with similar contributions from other 6d fields. We also discuss a 4d analog of the non-abelian self-dual model, which turns out to be UV finite., Comment: 25 pages; v2: minor corrections, references added; v3: typos fixed, published version

Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories., Comment: 5 pages

We consider the structure of current and stress tensor two-point functions in conformal field theory with a boundary. The main result of this paper is a relation between a boundary central charge and the coefficient of a displacement operator correlation function in the boundary limit. The boundary central charge under consideration is the coefficient of the product of the extrinsic curvature and the Weyl curvature in the conformal anomaly. Along the way, we describe several auxiliary results. Three of the more notable are as follows: (1) we give the bulk and boundary conformal blocks for the current two-point function; (2) we show that the structure of these current and stress tensor two-point functions is essentially universal for all free theories; (3) we introduce a class of interacting conformal field theories with boundary degrees of freedom, where the interactions are confined to the boundary. The most interesting example we consider can be thought of as the infrared fixed point of graphene. This particular interacting conformal model in four dimensions provides a counterexample of a previously conjectured relation between a boundary central charge and a bulk central charge. The model also demonstrates that the boundary central charge can change in response to marginal deformations., Comment: 75 pages, 4 figures; v2: references added. v3: comments on anomalous dimension and references added. v4: minor corrections, published version

Nanoporous graphitic carbon membranes with defined chemical composition and pore architecture are novel nanomaterials that are actively pursued. Compared to easy-to-make porous carbon powders that dominate the porous carbon research and applications in energy generation/conversion and environmental remediation, porous carbon membranes are synthetically more challenging though rather appealing from an application perspective due to their structural integrity, interconnectivity and purity. Here we report a simple bottom-up approach to fabricate large-size, freestanding, porous carbon membranes that feature an unusual single-crystal-like graphitic order and hierarchical pore architecture plus favorable nitrogen doping. When loaded with cobalt nanoparticles, such carbon membranes serve as high-performance carbon-based non-noble metal electrocatalyst for overall water splitting., Comment: 58 pages, 35 figures

The boundary Weyl anomalies live on a codimension-1 boundary, $\partial {\cal M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\Sigma$. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on $\partial {\cal M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure., Comment: 5+1 pages, 1 figure; v2: Improved discussion on a-type variation, conjecture RE=EE formulated to be independent of BCs imposed on matter fields, to appear in PRD Rapid Communications

Nanoporous carbon composite membranes, comprising a layer of porous carbon fiber structures with an average channel width of 30-60 nm grown on a porous ceramic substrate, are found to exhibit robust desalination effect with high freshwater flux. In three different membrane processes of vacuum membrane distillation, reverse osmosis and forward osmosis, the carbon composite membrane showed 100% salt rejection with 3.5 to 20 times higher freshwater flux compared to existing polymeric membranes. Thermal accounting experiments found that at least 80% of the freshwater pass through the carbon composite membrane with no phase change. Molecular dynamics simulations revealed a unique salt rejection mechanism. When seawater is interfaced with either vapor or the surface of carbon, one to three interfacial atomic layers contain no salt ions. Below the liquid entry pressure, the salt solution is stopped at the openings to the porous channels and forms a meniscus, while the surface layer of freshwater can feed the surface diffusion flux that is fast-transported on the surfaces of the carbon fibers, driven by the chemical potential gradient. As the surface-transported water does not involve a phase change, hence that component involves no energy expenditure in the form of latent heat.