Closed-form expression for cross-channel conformal blocks near the lightcone

We reviewed the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are solely based on symmetries, particularly on the analytic structure and in the associativity of the operator product expansion. We focused on two applications of the analytic conformal bootstrap: the study of the ϵ expansion of the Wilson–Fisher model via the introduction of a dispersion relation and the large N expansion of the maximally supersymmetric Super Yang–Mills theory in four dimensions.

We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE, (double) lightcone and Regge limits. Compatibility with the crossing equation imposes constraints on the functional kernels which we study in detail. We then introduce two simple classes of functionals. The first class has a simple action on generalized free fields and their deformations and can be used to bootstrap AdS contact interactions in general dimension. The second class is obtained by tensoring holomorphic and antiholomorphic copies of d = 1 functionals which have been considered recently. They are dual to simple solutions to crossing in d = 2 which include the energy correlator of the Ising model. We show how these functionals lead to optimal bounds on the OPE density of d = 2 CFTs and argue that they provide an equivalent rewriting of the d = 2 crossing equation which is better suited for numeric computations than current approaches.

In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\Delta$ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second-order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coefficients of primary operators in the limit where two of the operators are heavy.

Closed ecological systems (CES) represent a promising approach to long-term human life support (LS) for space expeditions and settlements such as a Mars manned expedition or a Lunar based research facility. In such remote, high risk ventures, sustainability and reliability of the integrated human-life support system (HLSS) are essential. However, facing possible overpopulation problem, Earth' environment can become more extreme for human beings in the nearest future. The biosphere of the Earth is a unique life support system (LSS). This relatively thin layer of biomass and other buffers provide all necessary conditions for all life forms' evolution, including humans. The biosphere can be viewed as highly reliable (during relatively short periods of time) self-sustainable system: life on Earth exists within a comparably narrow range of conditions for billions of years. All existing experimental facilities for research in the field of closed ecological life support systems (CELSS) such as BIOS-3M (Russia), Biosphere-2 (USA), CEEF (Japan) and others utilize principles and processes of bio-regeneration observed in the Biosphere of the Earth. Listed CELSS systems already demonstrated difficulty of sustainable and continuing life support functions implementations limited by insufficient (buffer) resources and incomplete closure of material recirculation. With the scattering of Earth's resources, humanity might meet similar problems on a global scale. Modeling (theoretical and experimental) of Earth's biosphere provides us with the tools for investigating such global processes in relatively short periods of time under controllable conditions which can be thoroughly monitored. Obvious benefits of artificial CELSS experiments are the possibilities for understanding global scale problems without irreversible harming of our planet's primary LSS - the biosphere. It became clear that classic control theory is only partially applied to closed ecosystems control. Therefore, understanding limits of stable functioning of CELSS and integrated study of control theory (including classic approach) which can propose certain solutions for control methods and algorithms are necessary. Nevertheless, the complete understanding of such complex problems caused by human population growth is impossible without integration of all existing fundamental methods of Earth sciences and experimental modeling based on small scale eco-spheres approach. This integrative approach opens at the same time a wide avenue for multiple international collaborations.

Single-line spectroscopic binaries have recently contributed to stellar-mass black hole discovery, independently of the X-ray transient method. We report the identification of a single-line binary system, LTD064402+245919, with an orbital period of 14.50 days. The observed component is a subgiant with a mass of 2.77 ± 0.68 M ⊙, radius 15.5 ± 2.5 R ⊙, effective temperature T eff 4500 ± 200 K, and surface gravity log g 2.5 ± 0.25 dex. The discovery makes use of the Large Sky Area Multi-Object fiber Spectroscopic Telescope time-domain and Zwicky Transient Facility survey. Our general-purpose software pipeline applies a Lomb–Scargle periodogram to determine the orbital period and uses machine learning to classify the variable type from the folded light curves. We apply a combined model to estimate the orbital parameters from both the light and radial velocity curves, taking constraints on the primary star mass, mass function, and detection limit of secondary luminosity into consideration. We obtain a radial velocity semiamplitude of 44.6 ± 1.5 km s−1, mass ratio of 0.73 ± 0.07, and an undetected component mass of 2.02 ± 0.49 M ⊙ when the type of the undetected component is not set. We conclude that the inclination is not well constrained, and that the secondary mass is larger than 1 M ⊙ when the undetected component is modeled as a compact object. According to our investigations using a Monte Carlo Markov Chain simulation, increasing the spectra signal-to-noise ratio by a factor of 3 would enable the secondary light to be distinguished (if present). The algorithm and software in this work are able to serve as general-purpose tools for the identification of compact objects quiescent in X-rays.

We study possible smooth deformations of the generalized free conformal field theory in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first nontrivial order in the ε expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.

We start a systematic study of quarter-BPS operators in four-dimensional mathcal{N} = 4 Super Yang-Mills with gauge group SU(N) making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures, and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large N supergravity limit and we make contact with the OPE limit of the five-point function of half-BPS operators.

In this paper, we study a class of sphere and torus correlation functions in the W N minimal model. In particular, we show that a large class of exact sphere three-point functions of W N primaries, derived using affine Toda theory, exhibit large N factorization. This allows us to identify some fundamental particles and their bound states in the holographic dual, including light states. We also derive the torus two-point function of basic primaries, by directly constructing the relevant conformal blocks. The result can then be analytically continued to give the Lorentzian thermal two-point functions.

We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin s non-conserved operators and a spin 1 conserved current. We give explicit expressions for the 3-point function when the two non-conserved operators have spins 1 and 2 and generic conformal dimensions. We also systematically analyse the divergences appearing in these 3-point functions when the conformal dimensions of the two non-conserved operators coincide.

We study the three-point energy correlator (EEEC), defined as a matrix element of a product of three energy detectors at different locations on the celestial sphere. Lorentz symmetry implies that the EEEC can be decomposed into special functions called celestial blocks. We compute three-point celestial blocks in an expansion around the collinear limit, where the three detectors approach each other on the celestial sphere. The leading term is a traditional d – 2-dimensional four-point conformal block, and thus the collinear EEEC behaves like a conformally-invariant four-point function in d – 2 dimensions. We obtain the coefficients of the conformal block decomposition for the collinear EEEC at leading nontrivial order in weakly-coupled \U0001d4a9 = 4 SYM and QCD. These data allow us to make certain all-orders predictions for the collinear EEEC in various kinematic limits, including the OPE limit and the double lightcone limit. We also study Ward identities satisfied by the EEEC and compute contact terms in the EEEC in weakly-coupled \U0001d4a9 = 4 SYM. Finally, we study the celestial block expansion of the EEEC in planar \U0001d4a9 = 4 SYM at strong coupling, determining celestial block coefficients to leading and first subleading order at large λ.

In this work we discuss an analytic bootstrap approach [1, 2] in the context of spinning 4D conformal blocks [3, 4]. As an example we study the simplest spinning case, the scalar-fermion correlator leftlangle phi psi phi overline{psi}rightrangle . We find that to every pair of primary scalar ϕ and fermion ψ correspond two infinite towers of fermionic large spin primary operators. We compute their twists and products of OPE coefficients using both s-t and u-t bootstrap equations to the leading and sub-leading orders. We find that the leading order is represented by the scalar-fermion generalized free theory and the sub-leading order is governed by the minimal twist bosonic (light scalars, currents and the energy-momentum tensor) and fermionic (light fermions and the suppersymmetric current) operators present in the spectrum.

We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between bulk and defect expansions. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate one-point functions of the twist defect of the 3d Ising model to first order in the ϵ-expansion.

CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry