Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours

Abstract

An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present results on the masses of several gauge singlet states as a function of the physical quark mass determined through the axial Ward identity and find indications of a change from chiral symmetry breaking to a phase consistent with conformal behaviour at beta_L ~ 2. However, the measurement of the spectrum is not alone sufficient to decisively confirm the existence of conformal fixed point in this theory as we show by comparing to similar measurements with fundamental fermions. Based on the results we sketch a possible phase diagram of this lattice theory and discuss the applicability and importance of these results for the future measurement of the evolution of the coupling constant.

Figures (9)

• Figure 1: The schematic $\beta$-function of a theory with an infrared fixed point (dash-dotted line, top), walking coupling (solid line, middle) and QCD-like running coupling (dashed line, below).
• Figure 2: Left panel: The plaquette expectation value at fixed values of the lattice coupling $\beta_L=4/g_{\textrm{bare}}^2$ as functions of the hopping parameter $\kappa$ for the theory with adjoint representation fermions. The measurements are done using $10^4$ lattices. Right panel: Same as left, but for the fundamental representation fermions.
• Figure 3: Left panel: The physical (PCAC) quark mass $m_Q$ as a function of the hopping parameter $\kappa$ for the theory with adjoint representation quarks. Right panel: Same as left but for fundamental representation fermions.
• Figure 4: The phase diagram on $(\beta_L,\kappa)$ -plane for the adjoint theory. Solid circles denote the measured (and extrapolated for $\beta_L \le 1.9$) critical hopping parameters $\kappa_c(\beta_L)$, where $m_Q = 0$. At $\beta_L \mathrel{\hbox{$<$$\sim$}} 2$ there appears a 1st order phase transition, which ends at a critical point shown by open square. The phase structure above the critical line is a conjecture, and it can be more complex than shown here. The Aoki phase may exist also for values larger than $\beta_L\sim 2$.
• Figure 5: Pseudoscalar ("$\pi$") mass for the adjoint representation quark theory at different values of $\beta_L$. The dotted line is a fit $\propto\sqrt{m_Q}$ to the mass measurements at $\beta_L \le 1.9$ and $m_Qa\le 0.5$.