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Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A glueing procedure welding the tiles back together is needed to return to the original object. In this note we present work in progress on n-point functions of BPS operators. In this case, quantum corrections are entirely carried by the glueing procedure. The lowest non-elementary process is the glueing of three adjacent tiles by the exchange of two single magnons. This problem has been analysed before. With a view to resolving some conceptional questions and to generalising to higher processes we are trying to develop an algorithmic approach using the representation of hypergeometric sums as integrals over Euler kernels.
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A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrodinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $rtoinfty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}rm{N}$, the resonance $^{15}rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}rm{Be}$ and $^{11}rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{rm F}$
We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these methods offers great computational advantage over traditional techniques involving feynman diagrams, especially at higher orders in the PN expansion. As a specific example, we reproduce the spin-orbit interaction up to 2.5 PN order as also the leading order $S^2$(3PN) hamiltonian for an arbitrary massive object. We also obtain the unknown $S^3$(3.5PN) spin hamiltonian for an arbitrary massive object in terms of its low frequency linear response to gravitational perturbations, which was till now known only for a black hole. Furthermore, we derive the missing $S^4$ Hamiltonian at leading order(4PN) for an arbitrary massive object and establish that a minimal coupling of a massive elementary particle to gravity leads to a black hole structure. Finally, the Kerr metric is obtained as a series in $G_N$ by comparing the action of a test particle in the vicinity of a spinning black hole to the derived potential.
We analyse the double-discontinuities of the four-point correlator of the stress-tensor multiplet in N=4 SYM at large t Hooft coupling and at order $1/N^4$, as a way to access one-loop effects in the dual supergravity theory. From these singularities we extract CFT-data by using two inversion procedures: one based on a recently proposed Froissart-Gribov inversion integral, and the other based on large spin perturbation theory. Both procedures lead to the same results and are shown to be equivalent more generally. Our computation parallels the standard S-matrix reconstruction via dispersion relations. In a suitable limit, the result of the conformal field theory calculation is compared with the one-loop graviton scattering amplitude in ten-dimensional IIB supergravity in flat space, finding perfect agreement.
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time. We also provide a strict model independent bound on the measure of quantum chaos, $-1/N(1-1/pi)leq {bf SFF}leq 0$ and $0leq {bf SFF}leq 1/pi N$, valid for thermal systems with a large and small number of degrees of freedom respectively. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos.
We consider the scattering matrices of massive quantum field theories with no bound states and a global $O(N)$ symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass $m$ transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity and $O(N)$ symmetry. We found a rich structure in that space by using convex maximization and in particular its convex dual minimization problem. At the boundary of the allowed space special geometric points such as vertices were found to correspond to integrable models. The dual convex minimization problem provides a novel and useful approach to the problem allowing, for example, to prove that generically the S-matrices so obtained saturate unitarity and, in some cases, that they are at vertices of the allowed space.
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