Infrared regime of SU(2) with one adjoint Dirac flavor

SU(2) gauge theory with one Dirac flavor in the adjoint representation is investigated on a lattice. Initial results for the gluonic and mesonic spectrum, static potential from Wilson and Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number are presented. The results found are not consistent with conventional confining behavior, pointing instead tentatively towards a theory lying within or very near the onset of the conformal window, with the anomalous dimension of the fermionic condensate in the range $0.9\lesssim {\gamma }_{*}\lesssim 0.95$. The implications of our work for building a viable theory of strongly interacting dynamics beyond the standard model are discussed.

Figure 1

The phase diagram of the theory, showing the average plaquette on a $4^4$ lattice at $1.4\le \beta \le 2.8$, $-1.7\le am\le -0.1$.

Figure 2

The histogram of the average Polyakov loop for all configurations belonging to the set shown in the label of each subfigure, for all spacetime directions. The single peaks indicate an unbroken center symmetry.

Figure 3

The history of the topological charge $Q$ for the indicated ensembles; other ensembles had similar properties.

Figure 4

Effective masses for the given states as a function of $t$ in lattice units on the D2 ensemble. A fit of the plateau is also displayed, together with the fit range.

Figure 5

The connected correlator and the full correlator (which includes both connected and disconnected contributions) in the scalar meson channel for the ensamble D2.

Figure 6

The $2^{+}$ scalar baryon and $0^{+}$ glueball masses, at $am=-1.51$, for the four lattice sizes considered.

Figure 7

The static fermion potential of four selected lattices.

Figure 8

Selected spectrum of the theory, showing meson, baryon, glueball, and spin-$\frac{1}{2}$ states, and ${\sigma }^{1/2}$.

Figure 9

Spectrum of the theory, showing meson, glueball, and spin-$\frac{1}{2}$ states, all normalized by ${\sigma }^{1/2}$.

Figure 10

Plots of $La{m}_{2^{+}}$ as a function of $La{m}_{\mathrm{PCAC}}^{1/(1+{\gamma }_{*})}$ for the three lattice volumes $24\times {12}^3$, $32\times {16}^3$ and $48\times {24}^3$ and ${\gamma }_{*}=0.9,1.0,1.1$ (top: ${\gamma }_{*}=0.9$; middle: ${\gamma }_{*}=1.0$; bottom: ${\gamma }^{*}=1.1$). The results appear to identify a universal curve for ${\gamma }_{*}=0.9–1.0$.

Figure 11

The behavior of the Dirac mode number for a subset of the lattices considered.

Figure 12

The behavior of the Dirac mode number on the D2 lattice, compared with the results of the numerical fit, with ${\gamma }_{*}=0.92$.

Figure 13

Plateaux for the fitted observables for the D2 data at various lengths and positions of the fitting window. The color represents the position of the lower end of the window, and the $x$ axis the upper end. The plateaux at the top-right of each plot were taken as the central values of our estimates.