The θ-dependence of the Yang-Mills spectrum from analytic continuation
Claudio Bonanno, Claudio Bonati, Mario Papace, Davide Vadacchino
Abstract
A bstract We study the θ -dependence of the string tension and of the lightest glueball mass in four-dimensional SU( N ) Yang-Mills theories. More precisely, we focus on the coefficients parametrizing the $$ \mathcal{O}\left({\theta}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>θ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> dependence of these quantities, which we investigate by means of numerical simulations of the lattice-discretized theory, carried out using imaginary values of the θ parameter. Topological freezing at large N is avoided using the Parallel Tempering on Boundary Conditions algorithm. We provide controlled continuum extrapolations of such coefficients in the N = 3 case, and we report the results obtained on two fairly fine lattice spacings for N = 6.