Global aspects of the renormalization group and the hierarchy problem

Abstract

The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09 ± 0.24GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. It is known that the hierarchy problem can be interpreted in terms of the near criticality between the two phases. The coefficient of the Higgs bilinear in the scalar potential, m 2 , is pushed by quantum corrections away from zero, towards the extremes of the interval [−M 2 P l , M 2 P l ] where M P l is the Planck mass. In this article, I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. In holographic terms, invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes.

A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

“…The two previous equations giveM M = −I (34) whereM ab = M ba . The canonical scalar and its conjugate momentum have the following expansion…”

“…This structure is capable of globally avoiding the sign problem and of reducing the complexity not by simply adding new fields, but by adding new fields such that a topologically non-trivial structure emerges that has the role of a topological anti-anomaly, namely an additional region of the manifold over which the paths will cancel precisely the terms that generate the sign problem on the original, unextended field manifold. The non-detectability of auxiliary topological structures has been discussed in [33,34].…”

Entanglement as a resource for naturalness

“…There is of course the approach I took in ref. [1] where I discussed the homological algebraic terms and the alteration of the composition operation of the renormalisation semigroup in the context of imposing topological invariance as suggested by string theoretical T-duality. However, going back to low energies while keeping T-duality manifest proved to be quite complicated.…”

“…Topological effects in the Renormalisation group have been studied in the context of T-duality in ref. [1]. There I showed that demanding invariance to changes of topology amounts to corrections to the Higgs mass that could restore naturalness.…”

On the T-dual renormalisation of entanglement entropy

“…Despite the fact that many such exclusively string phenomena have been described, the connection to low energy phenomenology has always been a weak point of string theory. It appears however that string geometry is related to low energy observations in more subtle ways [1]. One of the profoundly stringtheoretical effects is the T-duality.…”