A scalar potential from gauge condensation and its implications

We consider a scalar field $\varphi$ whose coupling to the kinetic term of a non-abelian gauge field is set at an UV scale $M$. Then the confinement of the gauge sector will induce a $\varphi$-dependent vacuum energy which generates a dimensionful potential for the scalar. It provides a good example of dynamical generation of a new physics scale below $M$ through the vacuum expectation value $⟨\varphi ⟩$. This mechanism may shed light on the origin of dark matter, or spontaneous symmetry breaking applicable to the electroweak symmetry.