abstract

Nontrivial topological structures of non-Abelian gauge fields were discovered in the 1970s. Instanton solutions, describing vacuum tunneling through topological barriers, have fermionic zero modes which are at the origin of ‘t Hooft effective Lagrangian. In the 1980s, instanton ensembles have been used to explain chiral symmetry breaking. In the 1990s, a large set of numerical simulations were performed deriving Euclidean correlation functions. The special role of scalar diquarks in nucleons and color superconductivity in dense quark matter has been elucidated. In these lectures, we discuss further developments of physics related to gauge topology. We show that the instanton–anti-instanton “streamline” configurations describe “sphaleron transitions” in high-energy collisions, which result in production of hadronic clusters with nontrivial topological/chiral charges. (They are not yet observed, but discussions of dedicated experiments at the LHC and RHIC are ongoing.) Another new direction is instanton effects in hadronic spectroscopy, both in the rest frame and on the light front. We will discuss their role in central and spin-dependent potentials, form factors and anti-quark nuclear “sea”. Finally, we summarize the advances in the semiclassical theory of deconfinement, and chiral phase transitions at finite temperature, in QCD, and in some of its “deformed” versions.

abstract

We study the theoretical foundations of the recently developed large-momentum effective theory (LaMET) approach to the transverse-momentum-dependent parton distribution function (TMDPDF). We first show that the quasi-TMDPDF can be consistently defined and it relates to the physical TMDPDFs through a factorization formula in the large-momentum limit. We show that the factorization involves the intrinsic soft function which is related to the off-lightcone soft functions for the Drell–Yan process and can be realized as a form factor. We also study properties of the off-lightcone soft functions, such as IR safety, analyticity, rapidity divergence, etc. Universality classes of the off-lightcone soft functions are discussed. Finally, we show that the intrinsic soft function can be extracted by combining a light-meson form factor with large-momentum transfer and quasi-TMD wave functions for the light meson.