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Register a new userk-string tensions in the 3-d SU(N) Georgi-Glashow model
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The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k is of the order of N, the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same k-dependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N-dependence. Finally, we consider the possible implications of our analysis for the SU(N) analogue of compact QED in four dimensions.
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The nature of the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model is investigated. Within the dimensional-reduction hypothesis, the properties of the transition are described by a two-dimensional vectorial Coulomb gas models of electric and magnetic charges. The resulting critical properties are governed by a generalized SU(N) sine-Gordon model with self-dual symmetry. We show that this model displays a massless flow to an infrared fixed point which corresponds to the Z$_N$ parafermions conformal field theory. This result, in turn, supports the conjecture of Kogan, Tekin, and Kovner that the deconfining transition in the 2+1-dimensional SU(N) Georgi-Glashow model belongs to the Z$_N$ universality class.
We study correlations functions of magnetic vortices $V$ and Polyakov loop $P$ operators in the 2+1 dimensional Georgi-Glashow model in the vicinity of the deconfining phase transition. In this regime the (dimensionally reduced) model is mapped onto a free theory of two massive Majorana fermions. We utilize this fermionic representation to explicitly calculate the expectation values of $V$ and $P$ as well as their correlators. In particular we show that the $VV$ correlator is large, and thus the anomalous breaking of the magnetic $U(1)$ symmetry is order one effect in the near critical region. We also calculate the contribution of magnetic vortices to the entropy and the free energy of the system.
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.
The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using quantum consistency conditions, the braiding matrix is found explicitly in the fundamental representation. This matrix is shown to be related to the Racah matrix for $U_t(SL(N))$. From calculating the four-point functions with the Knizhnik-Zamolodchikov equations, the deformation parameter $t$ is shown to be $t=exp({ipi /(k+N)})$ when the level $kge 2$. For $k=1$, there are two possible types of braiding, $t=exp({ipi /(1+N)})$ or $t=exp(ipi)$. In the latter case, the chiral vertex operators are constructed explicitly by extending the free field realisation a la Frenkel-Kac and Segal. This construction gives an explicit description of how to chirally factorise the $SU(N)_{k=1}$ WZW model.
We present here the results of our high accuracy simulations of $qbar q$ potential in $d=4$ SU(3) Yang-Mills theory. We measure this quantity by measuring the {it Polyakov Loop Correlators} using the {it exponential variance reduction technique(multilevel)} of Luscher and Weisz. We further use numerical integration of the one-link integrals of SU(3) theory by adopting techniques proposed by de Forcrand and Roiesnell achieving significant speed-up in the process. Measurements were done at $beta = 5.7$ on $24^3x32$ as well as $32^4$ lattices for separations between the Polyakov loops in the range $r = 2-9$ in lattice units. We analyse the results in terms of the force between $qbar q$ pair as well as in terms of a {em scaled second derivative} of the potential. We show that the data is accurate enough to distinguish between different string models and that it seems to favour the expression for ground state energy of a Nambu-Goto string. We conclude by discussing future plans.
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