Speaker
Description
We present a new rigorous scheme for understanding quark confinement based on the non-perturbative vacuum disordered by some topological defects. We start from the 4-dim. Euclidean Yang- Mills theory and require the conformal equivalence between the 4- dim.Euclidean space and the possible curved spacetimes with some compact dimensions. This requirement forces us to restrict the gauge configurations of 4-dim.Yang-Mills instantons to those with some space symmetries (called symmetric instantons) which are identified with magnetic monopoles and vortices living in the lower-dimensional curved spacetime with non-zero curvature through the dimensional reduction. The new scheme gives the direct built-in equivalence between (3-dim.hyperbolic) magnetic monopoles (of Atiyah type) and (2-dim.hyperbolic) vortices (of Witten-Manton type), which have been assumed without any rigorous proof to be the dominant contributors to quark confinement. This unified treatment of two topological defects is shown to give the semi-classical picture for quark confinement in the sense of Wilson. At the same time, this scheme caused by the dimensional reduction give a holographic description of magnetic monopole dominance on AdS3 in the rigorous way without any further assumptions. Moreover, the asymptotic freedom is also shown to be derived by performing the pertutbative deformation on the vacuum with these topological defects. [Paper in preparation to be submitted to ArXiv]
