k-String tensions and their large-N dependence

We consider whether the 1/N corrections to k-string tensions must begin at order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir Scaling, are also acceptable. The issue is important because different models of confinement differ in their predictions for the representation-dependence of k-string tensions, and corrections involving odd powers of 1/N would seem to be ruled out by the large-N expansion. We show, however, that k-string tensions may, in fact, have leading 1/N corrections, and consistency with the large-N expansion, in the open string sector, is achieved by an exact pairwise cancellation among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations come about in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action, in which k-string tensions follow the Casimir scaling rule.Comment: Talk presented at the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi

About Orientifold Planar Equivalence on the Lattice

The orientifold planar equivalence is the equivalence in the large-N limit of the bosonic sectors of the super Yang-Mills and the QCD with a quark in the antisymmetric representation. I give a sketch of the proof of the orientifold planar equivalence in the strong-coupling and large-mass phase on the lattice. It is still matter of discussion, if its validity extends also in the continuum limit

Conformal vs confining scenario in SU(2) with adjoint fermions

The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling $\beta = 4/g_0^2 = 2.25$ for values of the bare fermion mass $m_0$ that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near--)conformal and the confining scenario is outlined.Comment: 5 pages, 4 figures using RevTeX4, Typos corrected, references added. Versions to appear on PR

How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: the case of InAs/GaAs(001)

The two- to three-dimensional growth transition in the InAs/GaAs(001) heterostructure has been investigated by atomic force microscopy. The kinetics of the density of three dimensional quantum dots evidences two transition thresholds at 1.45 and 1.59 ML of InAs coverage, corresponding to two separate families, small and large. Based on the scaling analysis, such families are characterized by different mechanisms of aggregation, involving the change of the critical nucleus size. Remarkably, the small ones give rise to a wealth of "monomers" through the erosion of the step edges, favoring the explosive nucleation of the large ones.Comment: 10 pages, 3 figures. Submitted to Phys. Rev. Let

k-String tensions and the 1/N expansion

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.Comment: RevTeX4, 21 pages. Typos corrected, references added, some discussions expanded; conclusions unchanged. Version to appear on PR

Degeneracy Between the Regge Slope of Mesons and Baryons from Supersymmetry

We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the fermionic strings coincide. Our description of mesons and baryons as oriented and un-oriented bosonic and fermionic QCD-strings is in full agreement with the spectra of open strings in the dual type 0' string theory.Comment: v2: extended version. Appendices and references adde

Spontaneous breaking of discrete symmetries in QCD on a small volume

In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C), spatial reflection (P) and time reversal (T) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show that a physical signature for the symmetry breaking is a persistent baryonic current wrapping in the compact directions. The existence of such a current is derived analytically at first order in perturbation theory and confirmed in the non-perturbative regime by lattice simulations.Comment: 4 pages, 2 figures, based on the poster presented by B. Lucini at Pascos 0