We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher-Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment. Unlike the method of bosonization, the Fisher-Hartwig formula correctly takes into account the discreteness of charge. Furthermore, we check numerically the precision of the generalized Fisher-Hartwig formula, find that it has a higher precision than rigorously proven so far, and conjecture the form of the next-order correction to the existing formula. PACS numbers: 05.30.Fk, 05.40.-a, 02.50.-r arXiv:1108.1355v1 [cond-mat.str-el]

We correct Eq. (10) for deep inelastic scattering (DIS) through QCD instantons and its longitudinal as well as transverse projections. For the single spin asymmetries (SSA) in DIS with longitudinal polarizations, the corrected results fit better the reported data, while for the transversely polarized protons the results are larger than the experimentally reported data.

We model the soft pomeron in QCD using a scalar Polyakov string with extrinsic curvature in the bottom-up approach of holographic QCD. The overall dipole-dipole scattering amplitude in the soft pomeron kinematics is shown to be sensitive to the extrinsic curvature of the string for finite momentum transfer. The characteristics of the diffractive peak in the differential elastic pp scattering are affected by a small extrinsic curvature of the string.

We revisit the effects of QCD instantons in semi-inclusive deep inelastic scattering (SIDIS). We show that large single spin asymmetry (SSA) effects can be induced in longitudinally and transversely polarized proton targets. The results are in agreement with most of the reported data for pion and kaon production. The same effects are found to be important in polarized proton on proton scattering for both charged and chargeless pion productions. The results agree with the reported data in a wide range of √ s = 19.4 − 200 GeV. We predict the SSA for π ± production in p ↑ p in the collider range of √ s = 62.4 − 500 GeV. The backward π ± and π 0 productions for the SSA in p ↑ p collisions are predicted to coincide at large √ s.

In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang-Mills equation in the 3-and 4-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang-Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semi-classical level on a flat space with finite size or on a sphere.