Non perturbative simulations of quantum field theories using complex langevin dynamics

Abstract

Non-perturbative formulations of field theories are essential to capture numerous intrigu- newlineing physical phenomena, including confinement in quantum chromodynamics, spontaneous newlinesupersymmetry (SUSY) breaking, and dynamical compactification of extra dimensions in su- newlineperstring theories. Regularizing field theories on a spacetime lattice provides a robust frame- newlinework for studying their non-perturbative features. The underlying theory can be quantized newlineon a spacetime lattice using Euclidean path integrals. Conventionally, these path integrals newlineare evaluated using numerical methods based on Monte Carlo importance sampling, where newlinegenerating field configurations requires the Boltzmann factor to be interpreted as a proba- newlinebility weight. However, various interesting physical systems have complex actions, rendering newlinethe Boltzmann factor complex, and thus, path integral Monte Carlo encounters the sign newlineproblem. The complex Langevin method (CLM) based on stochastic quantization aims to newlineovercome the sign problem by analyzing the associated Langevin dynamics to evaluate com- newlineplex integrals. This thesis employs the CLM to investigate various non-perturbative aspects newlineof field-theoretic systems with complex actions. newlinePhysicists have long sought a unified description of all fundamental interactions of nature, newlineand SUSY is now widely accepted as a necessary ingredient for such unifying approaches. newlineHowever, since experimental evidence suggests that low-energy physics is manifestly non- newlinesupersymmetric, SUSY must be spontaneously broken at some energy scale. This thesis newlineprobes the possibility of spontaneous SUSY breaking in the simplest realizations of super- newlinesymmetric field theories. These systems generally have complex actions arising from a com- newlineplex determinant of the fermion operator, and the phase of the determinant plays a critical newlinerole in determining the correct vacuum. We studied various interesting classes of, in gen- newlineeral, complex superpotentials, including the ones exhibiting PT -symmetry. Non-Hermitian newlinePT -symmetric theories are