Generalized hydrodynamics of a (1+1)-dimensional integrable scattering theory with roaming trajectories

The emergence of hydrodynamic features in off-equilibrium (1 + 1)-dimensional integrable quantum systems has been the object of increasing attention in recent years. In this Master Thesis, we combine Thermodynamic Bethe Ansatz (TBA) techniques for finite-temperature quantum field theories with the Generalized Hydrodynamics (GHD) picture to provide a theoretical and numerical analysis of Zamolodchikov’s staircase model both at thermal equilibrium and in inhomogeneous generalized Gibbs ensembles. The staircase model is a diagonal (1 + 1)-dimensional integrable scattering theory with the remarkable property of roaming between infinitely many critical points when moving along a renormalization group trajectory. Namely, the finite-temperature dimensionless ground-state energy of the system approaches the central charges of all the minimal unitary conformal field theories (CFTs) M_p as the temperature varies. Within the GHD framework we develop a detailed study of the staircase model’s hydrodynamics and compare its quite surprising features to those displayed by a class of non-diagonal massless models flowing between adjacent points in the M_p series. Finally, employing both TBA and GHD techniques, we generalize to higher-spin local and quasi-local conserved charges the results obtained by B. Doyon and D. Bernard [1] for the steady-state energy current in off-equilibrium conformal field theories.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.