The Factorized S-Matrix of CFT/AdS

We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory's dilatation operator nor the string sigma model's quantum Hamiltonian, but instead the respective factorized S-matrix. To illustrate the idea, we focus on the closed fermionic su(1|1) sector of the N=4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector's three-loop S-matrix from Beisert's involved algebraic work on the three-loop su(2|3) sector. We then show that the current knowledge about semiclassical and near-plane-wave quantum strings in the su(2), su(1|1) and sl(2) sectors of AdS_5 x S^5 is fully consistent with the existence of a factorized S-matrix. Analyzing the available information, we find an intriguing relation between the three associated S-matrices. Assuming that the relation also holds in gauge theory, we derive the three-loop S-matrix of the sl(2) sector even though this sector's dilatation operator is not yet known beyond one loop. The resulting Bethe ansatz reproduces the three-loop anomalous dimensions of twist-two operators recently conjectured by Kotikov, Lipatov, Onishchenko and Velizhanin, whose work is based on a highly complex QCD computation of Moch, Vermaseren and Vogt.Comment: 38 pages, LaTeX, JHEP3.cl

Anomalous Scale Dimensions from Timelike Braiding

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the center of the conformal covering group $Z(\widetilde{SO(d,2)}),$ we explore the possibility of a timelike braiding structure consistent with the timelike ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in D=4 spacetime dimensions. Other ideas of constructions based on the $AdS_{5}$-$CQFT_{4}$ or the perturbative SYM approach in their relation to the present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages tcilatex, 3 latexcad figure

Physics Informed Neural Networks To Model The Hydro-Morphodynamics Of Mangrove Environments

Modelling the hydro-morphodynamics of mangrove environments is key for implementing successful protection and restoration projects in a climatically vulnerable region. Nevertheless, simulation of such dynamics is faced with computational and time constraints, given the nonlinear and complex nature of the problem, which could become a bottleneck for large-scale applications. The recent advances in machine learning, specifically, in physics-informed neural networks (PINNs), have gained much attention due to the potential to provide fast and accurate results, while preserving the binding physics laws and requiring small amounts of data in contrast to other neural networks. In this sense, such networks encode the physics equations into the neural network, and the latter must fit the noisy observed data whilst minimising the equation residual. This study investigates the application of PINNs to quantify the capacity of mangrove environments to attenuate waves and prevent erosion, and represents the first application of PINNs to model vegetation for a large-scale geographical domain with complex boundary conditions. Navier–Stokes, the broadly used mathematical equation to solve for fluid dynamics, is used as the governing equation that constrains the neural network to respect the conservation of mass, energy, and momentum. The Sundarbans, the largest mangrove forest in the world located between India and Bangladesh, is taken as a case study. The results demonstrate that the developed model is superior when compared to a numerical finite element model, in terms of time and data efficiency, yet produces equally strong overall results.</p