Abstract
We present a numerical study of three-dimensional two-color QCD with $N=0, 2, 4, 8$ and 12 flavors of massless two-component fermions using parity-preserving improved Wilson-Dirac fermions. A finite volume analysis provides strong evidence for the presence of $Sp(N)$ symmetry-breaking bilinear condensate when $N \le 2$ and its absence for $N \ge 8$. A weaker evidence for the bilinear condensate is shown for $N=4$. We estimate the critical number of flavors below which scale-invariance is broken by the bilinear condensate to be between $N=4$ and 6.
Highlights
Three-dimensional gauge theories coupled to an even number of two-component massless fermions can be regularized to form a parity-invariant theory
We have performed a numerical analysis of three dimensional SUð2Þ gauge theory coupled to an even number of massless fermions in such a way that parity is preserved
The price to pay was the absence of the full SpðNÞ flavor symmetry away from the continuum limit but this did not prevent us from extracting the critical number of fermion flavors
Summary
Three-dimensional gauge theories coupled to an even number of two-component massless fermions can be regularized to form a parity-invariant theory. The parityinvariant fermion action for N flavors of two-component fermions coupled to SUðNcÞ gauge-field Aμ is Z Sf 1⁄4. D3x X N=2 fφiðxÞCðAÞφiðxÞ þ χiðxÞC†ðAÞχiðxÞg; i1⁄41. Ð1Þ where CðAÞ is the two-component Dirac operator, with an ultraviolet regularization being imposed implicitly. CðAÞ 1⁄4 σμð∂μ þ iAμðxÞÞ; ð2Þ μ1⁄41 with σμ being the three Pauli matrices. One can think of the above parity-invariant theory of N flavors of two-component fermions to be equivalent to a theory of. N 2 flavors of fourcomponent fermions ψi with a Hermitian Dirac operator D: X N=2 Z Sf 1⁄4
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