Lattice Study of the Conformal Window in QCD-like Theories (original) (raw)
Conformal versus confining scenario in SU(2) with adjoint fermions
Physical Review D, 2009
The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling β = 4/g 2 0 = 2.25 for values of the bare fermion mass m0 that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.
Physical Review D, 2007
We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vector-like matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories developing an infrared stable fixed point. We find that exactly 50 % of the asymptotically free theories can develop an infrared fixed point while for the nonsupersymmetric theories it is circa 25 %. When considering multiple representations, only for the nonsupersymmetric case, the conformal regions quickly dominate over the nonconformal ones. For four representations, 70 % of the asymptotically free space is filled by the conformal region.
Features of a Simple IR Conformal Gauge Theory
The Schwinger model with N f ≥ 2 flavors is a simple example for a fermionic model with zero chiral condensate Σ (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Σ = 0, which include IR conformal theories. In particular we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD.
Hidden Conformal Symmetry from the Lattice
arXiv (Cornell University), 2023
We analyze newly expanded and refined data from lattice studies of an SU (3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of pseudoscalars and a single light scalar. We first consider the view that this theory is just outside the conformal window. In this case, the pseudoscalars arise from spontaneous breaking of chiral symmetry. Identifying the scalar in this case as an approximate dilaton, we fit the lattice data to a dilaton effective field theory, finding that it yields a good fit even at lowest order. For comparison, we then consider the possibility that the theory is inside the conformal window. The fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data, and find that it is of lesser quality.
Physical Review Letters, 2010
We study the chiral properties of an SU (3) gauge theory with N f massless Dirac fermions in the fundamental representation when N f is increased from 2 to 6. For N f = 2, our lattice simulations lead to a value of ψ ψ /F 3 , where F is the Nambu-Goldstone-boson decay constant and ψ ψ is the chiral condensate, which agrees with the measured QCD value. For N f = 6, this ratio shows significant enhancement, presaging an even larger enhancement anticipated as N f increases further, toward the critical value for transition from confinement to infrared conformality.
Conformal window of gauge theories with four-fermion interactions and ideal walking technicolor
Physical Review D, 2010
We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four-fermion interactions are neglected. The anomalous dimension of the mass increases beyond the unity value at the lower boundary of the new conformal window. We plot the new phase diagram which can be used, together with the information about the anomalous dimension, to propose ideal models of walking technicolor. We discover that when the extended technicolor sector, responsible for giving masses to the standard model fermions, is sufficiently strongly coupled the technicolor theory, in isolation, must have an infrared fixed point for the full model to be phenomenologically viable. Using the new phase diagram we show that the simplest one family and minimal walking technicolor models are the archetypes of models of dynamical electroweak symmetry breaking. Our predictions can be verified via first principle lattice simulations. * Electronic address: fukano@kmi.nagoya-u.ac.jp † Electronic address: sannino@cp3.sdu.dk 1 arXiv:1005.3340v1 [hep-ph]
Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
Physical Review D, 2009
We have performed numerical simulations of SU(3) gauge theory coupled to N f = 2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L = 6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.
Lattice study on QCD-like theory with exact center symmetry
Journal of High Energy Physics, 2015
We investigate QCD-like theory with exact center symmetry, with emphasis on the finite-temperature phase transition concerning center and chiral symmetries. On the lattice, we formulate center symmetric SU(3) gauge theory with three fundamental Wilson quarks by twisting quark boundary conditions in a compact direction (Z 3 -QCD model). We calculate the expectation value of Polyakov loop and the chiral condensate as a function of temperature on 16 3 × 4 and 20 3 × 4 lattices along the line of constant physics realizing m P S /m V = 0.70. We find out the first-order center phase transition, where the hysteresis of the magnitude of Polyakov loop exists depending on thermalization processes. We show that chiral condensate decreases around the critical temperature in a similar way to that of the standard three-flavor QCD, as it has the hysteresis in the same range as that of Polyakov loop. We also show that the flavor symmetry breaking due to the twisted boundary condition gets qualitatively manifest in the high-temperature phase. These results are consistent with the predictions based on the chiral effective model in the literature. Our approach could provide novel insights to the nonperturbative connection between the center and chiral properties.
Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
Physical Review D
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the β-function was recently reported in the theory [1] with uncertainty in the location of the critical gauge coupling inside the narrow [6.0 < g 2 * < 6.4] interval and widely accepted since as the strongest evidence for a conformal fixed point and scale invariance in the theory with model-building implications. Using the exact same renormalization scheme as the previous study, we show that no fixed point of the β-function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the N f = 12 model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD beta function for arbitrary flavor number are discussed with respect to our work.
Thermodynamic Study for Conformal Phase in Large Nf Gauge Theory
We investigate the chiral phase transition at finite temperature (T ) in colour SU(N c = 3) Quantum Chromodynamics (QCD) with six species of fermions (N f = 6) in the fundamental representation [1]. The simulations have been performed by using lattice QCD with improved staggered fermions. The critical couplings β c L for the chiral phase transition are observed for several temporal extensions N t , and the two-loop asymptotic scaling of the dimensionless ratio T c /Λ L (Λ L = Lattice Lambda-parameter) is found to be achieved for N t ≥ 6. Further, we collect β c L at N f = 0 (quenched), and N f = 4 at a fixed N t = 6 as well as N f = 8 at N t = 6, 12, the latter relying on our earlier study. The results are consistent with enhanced fermionic screening at larger N f .