Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks

TL;DR

This study maps the phase diagram of $SU(2)$ gauge theory with two adjoint Dirac flavors by performing a high-resolution lattice scan in the $(\beta,m)$ plane on $8^3\times16$ lattices, using the Wilson gauge action and adjoint fermions. It finds a line of first-order transitions for $\beta<\beta_c \sim 2.0$ that ends at a critical point, after which the boundary continues as the locus of minimum meson mass with $m_\pi$ and $m_\rho$ becoming light and nearly degenerate for $\beta>\beta_c$. The results are compatible with either a nontrivial infrared fixed point or very slow running (walking) dynamics, signaling dynamics distinct from QCD and with potential relevance to near-conformal technicolor models; however, finite-size effects necessitate larger-volume studies and step-scaling analyses to conclusively distinguish conformal from walking behavior. Overall, the work highlights the rich infrared dynamics of adjoint-representation gauge theories and motivates further lattice investigations to clarify their continuum limits and phenomenological implications.

Abstract

We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \sim 2.0. For beta > beta_c the phase boundary is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the pion and rho masses along the phase boundary to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.

Figures (8)

• Figure 1: Plaquette expectation values as a function of the bare fermion mass, along lines of constant lattice gauge coupling $\beta=4/g^2$. It can be seen that $\beta_c \approx 2$ marks a transition, below which a first order phase transition is seen as the quark mass is varied. We therefore find that close to the phase boundary, $\beta_c$ corresponds corresponds to a "bulk" transition, below which only a lattice phase exists. This can be understood in terms of the dynamical generation of an effective adjoint plaquette term in the gauge action, due to the radiative effects of nearly massless adjoint "quarks." Of course, for masses far enough away from the critical value the renormalization of the gauge action is relatively small and the adjoint term will not lead to a bulk transition.
• Figure 2: The latent heat, which appears to vanish in the $\beta \to 2$ limit.
• Figure 3: The "rho" mass $m_\rho a$, as a function of the bare Wilson fermion mass $m$, for three example values of the bare lattice coupling $\beta$. Note that as $\beta$ increases past the critical value $\beta_c \approx 2$, the $\rho$ mass on the phase boundary becomes small on the order of the inverse lattice size $1/L$. This is consistent with the $\rho$ becoming a massless state in the thermodynamic limit
• Figure 4: The pion mass squared for example values of $\beta$. The very sharp behavior as the bare mass is varied away from the phase boundary near $\beta=2$ stands in contrast to the rounding that would normally be expected from the effects of the finite size effects. The significant decrease in the slope of the line as one approaches the phase boundary is presumably due to $(m_\pi a)^2/(m a) \sim a$, with $a(\beta,m)$ having a significant $m$ dependence when the fermions are very light. This is particularly true since the contribution of the quarks to the running of the coupling is quite close to that of the gluons.
• Figure 5: Pion and rho masses along the phase boundary. Note that they become degenerate for $\beta \mathrel{\hbox{$>$} {\hbox{$\sim$}}} 2$.