N = 1 supersymmetric Yang-Mills theory and adjoint QCD on the lattice

In this work we study the low-energy physics of Yang-Mills theory (YM) coupled to adjoint matter by means of lattice Monte Carlo simulations. A main ingredient of our computations is the YM gradient flow (GF). The kernel of the flow operator smoothens the fields in such a way that correlators of local operators can be computed avoiding divergences and extra multiplicative renormalisations. The flow kernel can also be related to a renormalisation group (RG) transformation. This property allows to compute the scaling dimensions of operators with respect to variations of the energy scale. We exploit these two properties of the GF in order to study non-perturbative properties of YM with adjoint fermions (adjoint QCD). First, we study the case when the YM field is coupled to a single adjoint fermion, i.e the N=1 supersymmetric YM. It is the only QCD-like supersymmetric theory in the sense that it has no scalars, is asymptotically free, has a low-energy mass-gap, is confining, and shows fermion condensation. We study these properties at zero and finite temperatures for the SU(2) and SU(3) gauge groups. With the GF we are able to confirm the formation of a non-vanishing chiral condensate at zero temperature and its melting at higher temperatures. We also observe that chiral symmetry restoration and deconfinement occur at the same critical temperature. We moreover investigate SU(3) supersymmetric YM on a cylinder at different compactification radii. We compare the fate of confinement with the thermal case and measure the trace of the energy-momentum tensor, which gives us information about the Witten index. Depending on the number of flavours, adjoint QCD may lie inside the conformal window, i.e it may be a conformal field theory in the infrared. In this context, we use the GF and the lattice in order to measure the scaling of the mass anomalous dimension. The goal is to see hints for conformal behaviour and to determine the value of the critical anomalous dimension.