Related papers: The Pinch Technique at Two Loops
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
The resummation of soft gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions, which has been computed through two loops. The two-loop matrix is proportional to the one-loop matrix. Recently there have been…
We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely…
We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions…
Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity,…
We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it…
Diagrammatic techniques are invented to implement QCD gauge transformations. These techniques can be used to discover how gauge-dependent terms are cancelled among diagrams to yield gauge-invariant results in the sum. In this way a…
We probe the two-scale factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar field theories with…
We extend the notion of generalized unitarity cuts to accommodate loop integrals with higher powers of propagators. Such integrals frequently arise in for example integration-by-parts identities, Schwinger parametrizations and Mellin-Barnes…
We briefly review the status quo of the application of integrable systems techniques to the AdS/CFT correspondence in the large charge approximation, a rapidly evolving topic. Intricate string and gauge computations of, respectively,…
Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the exp and log operations present in the…
We use the pinch technique formalism to construct the gauge-independent off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian (QCD) gauge theories. The new key observation is that all contributions originating from…
The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop…
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the…
In this text we outline the motivation for developping a quantum $S$-matrix approach for the classical gravitational two-body scattering. As an application we briefly present the derivation of black-hole metrics in various dimensions.
Sinkhorn's alternative minimization algorithm applied to a positive $n\times n$ matrix converges to a doubly stochastic matrix. If the algorithm, applied to a $2\times 2$ matrix, converges in a finite number of iterations, then it converges…
We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto…
We investigate the divergence structure of one-loop corrections to S and T parameteres in gauge-Higgs unification. We show that these parameters are finite in five dimensions, but divergent in more than five dimensions. Remarkably, a…
A simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal…