Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory

Abstract

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative computations.

Behaviour of the topological susceptibility in two colour QCD across the finite density transition

“…Actually this event seldom happens because the topological modes are effectively decoupled from the UV modes so that after starting from a classical configuration of any fixed topological content, it is difficult to alter the background topological sector by applying some updating (heating) steps at the corresponding value of β to thermalize the UV fluctuations. In fact this decoupling of the two types of modes is the gist of the heating method [60,61].…”

“…The rest of the contact divergences, if any, must be subtracted. This subtraction is M. In order to calculate it, we can follow the strategy introduced in [61,14]: M is the value of χ L in the sector of zero total topological charge, M ≡ χ L Q=0 . This prescription guarantees the physical requirement that χ vanishes in such a sector.…”

“…Since we will present the res- ults for the ratio χ(µ)/χ(µ = 0) as a function of µ, the multiplicative Z needed not be calculated (the notation χ(µ) indicates the physical topological susceptibility at a value µ of the chemical potential). Instead M was calculated by use of the heating method [60,61].…”

Analyticity in θ and infinite volume limit of the topological susceptibility in SU(3) gauge theory

“…where a is the lattice spacing, Z and M are renormalization constants that can be extracted by using a nonperturbative method [10,11]. In Eq.…”

“…We are currently calculating Z and M following the method of [10,11]. High statistics is required to reduce the errors.…”