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Causal Dynamical Triangulations provide a non-perturbative regularization of a theory of quantum gravity. We describe how this approach connects with the asymptotic safety program and Ho\vrava-Lifshitz gravity theory, and present the most recent results from computer simulations.
Lattice field theories with complex actions are not easily studied using conventional analytic or simulation methods. However, a large class of these models are invariant under CT, where C is charge conjugation and T is time reversal, including models with non-zero chemical potential. For Abelian models in this class, lattice duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.
The charmonium states at non-zero temperature are studied on anisotropic lattices with 2 dynamical quark flavours. Non-local operators are used to determine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional fitting methods and the Maximum Entropy Method. The interquark potential is determined from the solution of the Schrodinger equation, given the NBS wavefunction as input following the HAL QCD method. We observe a temperature dependent potential which becomes steeper as the temperature decreases.
I consider a reformulation of QCD which incorporates additional bosonic fields, and analyze it in the large-N limit. This construction makes a more direct connection with the nonrelativistic quark and the chiral quark models, as well as the bag model for baryons. This extension of QCD is neither a model nor an effective low energy theory, but is exactly equivalent to QCD.
I discuss the impact of the discovery of a Higgs-like state on composite dynamics starting by critically examining the reasons in favour of either an elementary or composite nature of this state. Accepting the standard model interpretation I re-address the standard model vacuum stability within a Weyl-consistent computation. I will carefully examine the fundamental reasons why what has been discovered might not be the standard model Higgs. Dynamical electroweak breaking naturally addresses a number of the fundamental issues unsolved by the standard model interpretation. However this paradigm has been challenged by the discovery of a not-so-heavy Higgs-like state. I will therefore review the recent discovery \cite{Foadi:2012bb} that the standard model top-induced radiative corrections naturally reduce the intrinsic non-perturbative mass of the composite Higgs state towards the desired experimental value. Not only we have a natural and testable working framework but we have also suggested specific gauge theories that can realise, at the fundamental level, these minimal models of dynamical electroweak symmetry breaking. These strongly coupled gauge theories are now being heavily investigated via first principle lattice simulations with encouraging results. The new findings show that the recent naive claims made about new strong dynamics at the electroweak scale being disfavoured by the discovery of a not-so-heavy composite Higgs are unwarranted. I will then introduce the more speculative idea of extreme compositeness according to which not only the Higgs sector of the standard model is composite but also quarks and leptons, and provide a toy example in the form of gauge-gauge duality.
We determine the quark-hadron transition line in the whole region of temperature (T) and baryon-number chemical potential (μ_B) from lattice QCD results and neutron-star mass measurements, making the quark-hadron hybrid model that is consistent with the two solid constraints. The quark part of the hybrid model is the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with entanglement vertex that reproduces lattice QCD results at mu_B/T=0, while the hadron part is the hadron resonance gas model with volume-exclusion effect that reproduces neutron-star mass measurements and the neutron-matter equation of state calculated from two- and three-nucleon forces based on the chiral effective field theory. The lower bound of the critical mu_B of the quark-hadron transition at zero T is mu_B = 1.6 GeV. The interplay between the heavy-ion collision physics around mu_B/T =6 and the neutron-star physics where mu_B/T is infinity is discussed.
Higher order moments of net conserved charge fluctuations, in particular net baryon number and net electric charge, are sensitive thermodynamic observables that respond strongly to critical behavior in strong interaction matter. In order to use them also as a sensible probe to detect critical behavior in heavy ion experiments we not only need to better understand the relation between chemical freeze-out in heavy ion collision and the QCD phase boundary, we also need to verify that charge fluctuations measured experimentally indeed correspond to thermal conditions as described by equilibrium QCD. This requires a model independent characterization of thermal conditions for which cumulants of conserved charge fluctuations themselves are ideally suited.
Correlation functions provide information on the properties of mesons in vacuum and of hot nuclear matter. In this Letter, we present a new method to derive a well-defined spectral representation for correlation functions. Combining this method with the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation, we calculate in-vacuum masses of light mesons and the electrical conductivity of the quark-gluon plasma. The analysis can be extended to other observables of strong-interaction systems.
The study of the CKM matrix elements with increasing precision requires a reliable evaluation of hadronic matrix elements of axial and vector currents which can be done with Lattice QCD. The tiniest entry, |V_{ub}|, can be estimated independently from B to tau nu and B to pi l nu decays. The ALPHA collaboration has undertaken the effort to evaluate non-perturbatively the decay constant f_B and the f^+(q) form factor for q^2 close to q_{max}^2 entering these determinations. Since for the b quark m_b >> a^{-1} for available lattice sizes, an effective description of the b quark is necessary. HQET provides an example of the latter. As any effective theory, HQET is predictive only when a set of parameters have been determined through a process called matching. The non-perturbative matching procedure applied by the ALPHA collaboration consists of 19 matching conditions needed to fix all the relevant parameters at order 1/m_B of the HQET action and the axial and vector currents. We present a study of one-loop corrections to two representative matching conditions. Our results enable us to quantify the quality of the observables used in the matching procedure.
We make a theoretical study of $ππ$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually considered. We quantify such effects by means of two different approaches for vector-isovector $ππ$ scattering based on Unitarized Chiral Perturbation Theory results: the Inverse Amplitude Method and another one based on the $N/D$ method. We take into account finite box effects stemming from higher orders through loops in the crossed $t,u-$channels as well as from the renormalization of the coupling constants. The main conclusion is that for $ππ$ phase shifts in the isovector channel one can safely apply Lüscher based methods for finite box sizes of $L$ greater than $2 m_π^{-1}$.
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=λNL and an angle defined in terms of the magnetic flux (λ is 't Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (NL dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
In lattice QCD computations a substantial amount of work is spent in solving linear systems arising in Wilson's discretization of the Dirac equations. We show first numerical results of the extension of the two-level DD-αAMG method to a true multilevel method based on our parallel MPI-C implementation. Using additional levels pays off, allowing to cut down the core minutes spent on one system solve by a factor of approximately 700 compared to standard Krylov subspace methods and yielding another speed-up of a factor of 1.7 over the two-level approach.
We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents $β/ν$ and $ω$ associated with the quantum phase transition induced by dimerization are determined with high precision. Here $β$ and $ν$ are the exponents related to the magnetization and the correlation length, respectively. In addition, $ω$ is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of $ω$ compatible with the known result in the O(3) universality class. Further, using either the value of $ω$ determined here or the established one in the literature, the exponent $β/ν$ calculated from our data is in quantitative agreement with the known result $β/ν= 0.519(1)$ as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.
We use Lattice QCD calculations of fluctuations and correlations of various conserved charges to show that the deconfinement of strangeness takes place in the chiral crossover region of QCD; however, inside the quark-gluon plasma strange quarks remain strongly interacting at least up to temperatures twice the QCD crossover temperature. Further, we discuss how the freeze-out parameters of heavy-ion collisions can be determined in a model-independent way through direct comparisons between experimentally measured higher order cumulants of conserved charges and corresponding Lattice QCD calculations. Utilizing the preliminary data from the STAR and PHENIX experiments we illustrate this method. Although, the Lattice QCD based determinations of the freeze-out parameters utilizing data sets of different experiments and different observables are currently not consistent with each other, it is tantalizing to see that all the observed freeze-out parameters lie very close to the chiral/deconfinement crossover region of QCD.
We provide outstanding numerical evidence that in large-N massless QCD the joint spectrum of the masses squared, for fixed integer spin s and unspecified parity and charge conjugation, obeys exactly the following laws: m_k^2 = (k+s/2) Lambda_QCD^2 for s even, m_k^2 = 2(k+s/2) Lambda_QCD^2 for s odd, k = 1,2,... for glueballs, and m_n^2 = 1/2 (n+s/2) Lambda_QCD^2, n = 0,1,... for mesons. One of the striking features of these laws is that they imply that the glueball and meson masses squared form exactly-linear Regge trajectories in the large-N limit of massless QCD, all the way down to the low-lying states: A fact unsuspected so far. The numerical evidence is based on lattice computations by Meyer-Teper in SU(8) YM for glueballs, and by Bali et al. in SU(17) quenched massless QCD for mesons, that we analyze systematically. The aforementioned spectrum for spin-0 glueballs is implied by a Topological Field Theory underlying the large-N limit of YM, whose glueball propagators satisfy as well fundamental universal constraints arising from the asymptotic freedom and the renormalization group. No other presently existing model meets both the infrared spectrum and the ultraviolet constraints. We argue that some features of the aforementioned spectrum of glueballs and mesons of any spin could be explained by the existence of a Topological String Theory dual to the Topological Field Theory.
We construct a four dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of a $SU(2)\times SU(2)$ gauge symmetry. This fermion representation ensures that single site bilinear mass terms vanish identically. A symmetric four fermion operator is however allowed and we show numerical results that show that a condensate of this operator develops in the vacuum.
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.
We compute next-to-leading order (NLO) corrections in the ε-regime of Wilson (WChPT) and Staggered Chiral Perturbation Theory (SChPT). A difference between the two is that in WChPT already at NLO, that is at O(ε^2), new low energy constants (LECs) contribute, whereas in SChPT they only enter at O(ε^4). We first determine the NLO corrections in WChPT for SU(2), and for U(N_f) at fixed index. This implies finite-volume corrections to the phase boundary between the Aoki phase and the Sharpe-Singleton scenario via corrections to the mean field potential. We also compute NLO corrections to the two-point function in the scalar and pseudo-scalar sector in WChPT. Turning to SChPT we determine the NLO corrections to the LECs and their effect on the taste splitting. Here the NLO partition function can be written as the leading order one with renormalized couplings, thus preserving the equivalence to staggered chiral random matrix theory at NLO for any number of flavors N_f. In WChPT this relation only appears to hold for SU(2).