Abstract
Abstract We present details of a lattice study of infrared behaviour in SU(3) gauge theory with twelve massless fermions in the fundamental representation. Using the step-scaling method, we compute the coupling constant in this theory over a large range of scale. The renormalisation scheme in this work is defined by the ratio of Polyakov loop correlators in the directions with different boundary conditions. We closely examine systematic effects, and find that they are dominated by errors arising from the continuum extrapolation. Our investigation suggests that SU(3) gauge theory with twelve flavours contains an infrared fixed point.
Highlights
In recent years, there has been a significant amount of work in search of gauge theories viable for walking-technicolour model building
We present details of a lattice study of infrared behaviour in SU(3) gauge theory with twelve massless fermions in the fundamental representation
We present our work on the lattice study of IR behaviour in SU(3) gauge theory with twelve flavours
Summary
We give the details of our definition of the renormalised coupling constant in the twisted-Polyakov-loop (TPL) scheme [50, 51]. In order to maintain gauge invariance and single-valuedness of the fermion field, ψ(n + xLx/a + yLy/a), under the application of two boundary twistings (in xand ydirections) with different orderings, it is necessary to introduce the “smell” degrees of freedom [60]. This quantum number is carried by fermions. As explained it is important to control the continuum extrapolation in the step-scaling study of the running coupling constant This makes the use of the TPL scheme very desirable.
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