Nearly Conformal Gauge Theories on the Lattice (original) (raw)

Chiral symmetry breaking in fundamental and sextet fermion representations of SU(3) color

2011

We report new results for lattice gauge theories with twelve fermion flavors in the fundamental representation and two fermion flavors in the two-index symmetric (sextet) representation of the SU(3) color gauge group. Both models are important in searching for a viable composite Higgs mechanism in the Beyond the Standard Model (BSM) paradigm. We subject both models to opposite hypotheses inside and outside of the conformal window. In the first hypothesis we test chiral symmetry breaking ($\chi{\rm SB}$) with its Goldstone spectrum, FpiF_\piFpi, the chirmSB\chi{\rm SB}chirmSB condensate, and several composite hadron states as the fermion mass is varied in a limited range with our best effort to control finite volume effects. Supporting results for chirmSB\chi{\rm SB}chirmSB from the running coupling based on the force between static sources is also presented. In the second test for the alternate hypothesis we probe conformal behavior driven by a single anomalous mass dimension under the assumption of unbroken c...

Topology and chiral symmetry breaking in SU(Nc) gauge theories

Physical Review D, 2002

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SU (N c ) gauge theories with N c = 2, 3, 4 and 5 colours. We define a fermionic topological charge from the zero-modes of this operator and show that, as N c grows, any disagreement with the topological charge obtained by cooling the fields, becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about ρ ≃ 2.5a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger N c .

Further discussions on a possible lattice chiral gauge theory

Physics Letters B, 1997

In a possible SU L (2) lattice chiral gauge theory with a large multifermion coupling, we try to further clarify the threshold phenomenon: the possibility that the right-handed three-fermion state turns into the virtual states of its constituents (free chiral fermions) in the low-energy limit. Provided this phenomenon occurs, we discuss the chiral gauge coupling, Ward identities and the gauge anomaly within the gauge-invariant prescription of the perturbative chiral gauge theory.

Nearly conformal gauge theories in finite volume

Physics Letters B, 2009

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group as the number of fermion flavors is varied in the N f = 4 − 16 range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.

Realizations of chiral symmetry in a spontaneously broken lattice gauge theory

Physics Letters B, 1986

The phase diagram of lattice SU(2) gauge theory with fundamental representation Higgs fields is probed by /= 1/2 and 1=1 fermions. Quenched calculations of (~)l show two distinct regions characterized by broken or unbroken chiral symmetry. The location of the boundary between the two regions depends on the representation l of the fermions. For l = 1/2 fermions the presence is verified of Nambu-Goldstone bosons ("pions") in the broken region and evidence is found for massless physical fermions in the chirally symmetric region. Effects of boundary conditions and the possibility of observing two particle cuts in finite lattice spectrum calculations are commented on also.

The breaking of chiral gauge symmetry

Physics Letters B, 1989

We consider the possibility that the lack of a chiral gauge symmetry-preserving regulator is signaling a genuine quantum effect which breaks the chiral gauge symmetry and generates mass for the gauge bosons. A nonperturbative analysis of an SU(3)cxSU(2)L>(U(l)v model regularized on a lattice is presented. Although both SU(2)L and U(1)r symmetries in this model are broken in the regularized action, SU (3)c X U (1)o symmetry can be maintained throughout the calculations. Using a hopping parameter expansion, the effective action for the gauge bosons is derived. Mass terms for the gauge bosons are generated, and the mass ratio of the gauge bosons is discussed.

Lattice Study of the Conformal Window in QCD-like Theories

Physical Review Letters, 2008

We study the extent of the conformal window for an SU(3) gauge theory with N f Dirac fermions in the fundamental representation. We present lattice evidence for 12 ≤ N f ≤ 16 that the infrared behavior is governed by a fixed point, while confinement and chiral symmetry breaking are present for N f ≤ 8.

A Possible Lattice Chiral Gauge Theory

1996

We analyze the dynamics of an SU L (2)⊗U R (1) chiral gauge theory on a lattice with a large multifermion coupling 1 ≪ g 2 < ∞. It is shown that no spontaneous symmetry breaking occurs; the "spectator" fermion ψ R (x) is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral gauge symmetry. Whether right-handed three-fermion states disappear and chiral fermions emerge in the low-energy limit are discussed. Provided right-handed three-fermion states disappear, we discuss the chiral gauge coupling, Ward identities, the gauge anomaly and anomalous U L (1) global current within the gaugeinvariant prescription of renormalization of the gauge perturbation theory.

Nearly conformal electroweak sector with chiral fermions

Arxiv preprint arXiv: …, 2008

SU(3) gauge theory with dynamical overlap fermions in the 2-index symmetric (sextet) representation is considered. This model may be a viable model of the electroweak symmetry breaking sector along the lines of the walking technicolor paradigm. The number of fermion species is chosen such that the theory is expected to be below the conformal window. We will discuss how the ε-regime and random matrix theory can be used to test whether at any given set of parameters (N c , N f , representation) the theory is in the conformal phase or indeed just below it. Quenched Monte Carlo results are included in the fundamental representation and also preliminary dynamical ones in the 2-index symmetric representation.