Particle theory

Abstract:

We find a strong-to-weak coupling crossover in D=2+1 SU(N) lattice gauge theories that appears to become a third-order phase transition at N=∞, in a similar way to the Gross-Witten transition in the D=1+1 SU(N→∞) lattice gauge theory. There is, in addition, a peak in the specific heat at approximately the same coupling that increases with N, which is connected to ZN monopoles (instantons), reminiscent of the first-order bulk transition that occurs in D=3+1 lattice gauge theories for N≥5. Our calculations are not precise enough to determine whether this peak is due to a second-order phase transition at N=∞ or to the third-order phase transition having a critical behavior different to that of the Gross-Witten transition. We show that as the lattice spacing is reduced, the N=∞ gauge theory on a finite 3-torus appears to undergo a sequence of first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories. We investigate whether the trace of the Wilson loop has a nonanalyticity in the coupling at some critical area, but find no evidence for this. However we do find that, just as one can prove occurs in D=1+1, the eigenvalue density of a Wilson loop forms a gap at N=∞ at a critical value of its trace. We show that this gap formation is in fact a corollary of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops. © 2006 The American Physical Society.

Abstract:

We study the predictions of holographic QCD for various observable four-point quark flavour current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3)_L \times SU(3)_R$ Yang Mills theory in a slice of $AdS_5$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3)_V$ subgroup. We explain in detail how to calculate the 4D four-point quark flavour current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $\Delta I = 1/2$ rule for kaon decays and the $B_K$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.