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We explore an alternative discretization of continuum SU(N_c) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N_b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N_b can be as small as N_c. In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N_c) to SU(N_c), (ii) derive refined bounds on N_b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.
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We numerically explore an alternative discretization of continuum $text{SU}(N_c)$ Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group $text{U}(N_c)$. This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over $N_b$ auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum $text{SU}(N_c)$ Yang-Mills theory in $d=2$ dimensions if $N_b$ is larger than $N_c-frac{3}{4}$ and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for $d>2$. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group $text{SU}(2)$ in three dimensions. We show that observables computed in the induced theory, such as the static $qbar q$ potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find that the bound for $N_b$ can be relaxed to $N_c-frac{5}{4}$ as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.
QCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a controlled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed N_t approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly.
We perform a high precision measurement of the static $qbar{q}$ potential in three-dimensional SU($N$) gauge theory with $N=2,3$ and compare the results to the potential obtained from the effective string theory. In particular, we show that the exponent of the leading order correction in $1/R$ is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficient $bar{b}_2$, including an extensive analysis of all types of systematic uncertainties. We find that the magnitude of $bar{b}_2$ decreases with increasing $N$, leading to the possibility of a vanishing $bar{b}_2$ in the large $N$ limit. In the standard form of the effective string theory possible massive modes and the presence of a rigidity term are usually not considered, even though they might give a contribution to the energy levels. To investigate the effect of these terms, we perform a second analysis, including these contributions. We find that the associated expression for the potential also provides a good description of the data. The resulting continuum values for $bar{b}_2$ are about a factor of 2 smaller than in the standard analysis, due to contaminations from an additional $1/R^4$ term. However, $bar{b}_2$ shows a similar decrease in magnitude with increasing $N$. In the course of this extended analysis we also obtain continuum results for the masses appearing in the additional terms and we find that they are around twice as large as the square root of the string tension in the continuum and compatible between SU(2) and SU(3) gauge theory. In the follow up papers we will extend our investigations to the large $N$ limit and excited states of the open flux tube.
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
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 x 4 and 20^3 x 4 lattices along the line of constant physics realizing $m_{PS}/m_{V}=0.70$. 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.
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