  The understanding of phenomena falling outside the Ginzburg-Landau paradigm
of phase transitions represents a key challenge in condensed matter physics. A
famous class of examples is constituted by the putative deconfined quantum
critical points between two symmetry-broken phases in layered quantum magnets,
such as pressurised SrCu$_2$(BO$_3$)$_2$. Experiments find a weak first-order
transition, which simulations of relevant microscopic models can reproduce. The
origin of this behaviour has been a matter of considerable debate for several
years. In this work, we demonstrate that the nature of the deconfined quantum
critical point can be best understood in terms of a novel dynamical mechanism,
termed Nordic walking. Nordic walking denotes a renormalisation group flow
arising from a beta function that is flat over a range of couplings. This gives
rise to a logarithmic flow that is faster than the well-known walking
behaviour, associated with the annihilation and complexification of fixed
points, but still significantly slower than the generic running of couplings.
The Nordic-walking mechanism can thus explain weak first-order transitions, but
may also play a role in high-energy physics, where it could solve hierarchy
problems.
  We analyse the Wess-Zumino-Witten field theory pertinent to deconfined
quantum critical points with a topological term in 2+1 dimensions. To this end,
we construct an advanced functional renormalisation group approach based on
higher-order regulators. We thereby calculate the beta function directly in 2+1
dimensions and provide evidence for Nordic walking.
