Abstract
In this work we present the results of a numerical investigation of SU(2) gauge theory with Nf = 3/2 flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the fundamental fermion mass, represented by the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension γ∗ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac operator. The difference of the estimates at the two gauge couplings should be due to scaling violations and lattice spacing effects. The more reliable estimate at the smaller gauge coupling is γ∗ ≈ 0.38(2).
Highlights
QCD-like and approximate solutions of the Schwinger-Dyson equations, Dietrich and Sannino [3] have mapped out the phase diagram for non-supersymmetric theories with fermions in different representations of the gauge group SU(N ) as a function of N and Nf
In this work we present the results of a numerical investigation of SU(2) gauge theory with Nf = 3/2 flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group
We have investigated the masses of various particles, including mesons, glueballs and spin 1/2 fermion-glue bound states, the string tension, and the mass anomalous dimension, in order to gain insights into the IR behaviour of the theory
Summary
We consider SU(2) gauge theory coupled to fermions transforming under the adjoint representation of the gauge group. The eigenvalue distribution for these runs does not completely match the bounds of the polynomial approximation, but they can still be used to check the general properties of the sign problem in this theory without determining the otherwise necessary correction factors on the configurations. We observe that even at these critical parameters no negative sign is obtained for the measured configurations and a gap in the imaginary part Wilson-Dirac eigenvalues around zero appears. For generating field configurations on the lattice we have used the two-step polynomial hybrid Monte Carlo (PHMC) algorithm [12]. It is based on polynomial approximations of the inverse powers of the Wilson-Dirac matrix. The resulting two-step approximation is so good that no further correction by a reweighting factor is necessary in practice
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