No Arabic abstract
The (2+1)D Georgi-Glashow (or Polyakov) model with the additional fundamental massless quarks is explored at finite temperature. In the case of vanishing Yukawa coupling, it is demonstrated that the interaction of a monopole and an antimonopole in the molecule via quark zero modes leads to the decrease of the Berezinsky-Kosterlitz-Thouless critical temperature when the number of quark flavors is equal to one. If the number of flavors becomes larger, monopoles are shown to exist only in the molecular phase at any temperatures exceeding a certain exponentially small one. This means that for such a number of flavors and at such temperatures, no fundamental matter can be confined by means of the monopole mechanism.
We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions $langle sigmasigma rangle$ and $langle epsilonepsilon rangle$. As a result, we estimate the one-point functions of the lowest-dimension $mathbb Z_2$-even scalar $epsilon$ and the stress-energy tensor $T_{mu u}$. Our result for $langle sigmasigma rangle$ at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.
We investigate the properties of the twist line defect in the critical 3d Ising model using Monte Carlo simulations. In this model the twist line defect is the boundary of a surface of frustrated links or, in a dual description, the Wilson line of the Z2 gauge theory. We test the hypothesis that the twist line defect flows to a conformal line defect at criticality and evaluate numerically the low-lying spectrum of anomalous dimensions of the local operators which live on the defect as well as mixed correlation functions of local operators in the bulk and on the defect.
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.
How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly $(d-1)$, whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound $Delta_V>5.0$ on the scaling dimension of the lowest virial current candidate $V$, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.
We study the finite-temperature properties of the supersymmetric version of (2+1)D Georgi-Glashow model. As opposed to its nonsupersymmetric counterpart, the parity symmetry in this theory at zero temperature is spontaneously broken by the bilinear photino condensate. We find that as the temperature is raised, the deconfinement and the parity restoration occur in this model at the same point $T_c=g^2/8pi$. The transition is continuous, but is not of the Ising type as in nonsupersymmetric Georgi-Glashow model, but rather of the Berezinsky-Kosterlitz-Thouless type as in $Z_4$-invariant spin model.