6 papers
Superloop Equations and Minimal Surfaces I: Confining minimal surface in SYM
Alexander Migdal
We formulate the loop equations of pure super Yang--Mills (SYM) theory in a finite geometric form. The usual equal-point loop derivatives are singular because the order o…
Geometric QCD III: Exact transition amplitudes and the glueball spectrum
Alexander Migdal
We complete the analysis of planar Makeenko--Migdal loop equations in the Lorentz-invariant continuum limit. Using our confining twistor-string representation, we compute the quant…
Geometric QCD II: The Confining Twistor String and Meson Spectrum
Alexander Migdal
We present a local, asymptotically free solution of the planar Makeenko--Migdal loop equations in the continuum limit with full Lorentz invariance. The solution is constructed by q…
Geometric QCD I: The Hodge-Dual Surface and Quark Confinement
Alexander Migdal
This is the first of two papers presenting a geometric framework for Planar QCD (). In this part, we establish the kinematic foundation of the theory by constructin…
Spontaneous quantization of the Yang--Mills gradient flow
Alexander Migdal
We formulate a nonsingular loop-space calculus for Yang-Mills (YM) gradient flow directly in terms of Wilson loops. Variations act within the manifold of smooth loops via finite, r…
Exact Confining Solution of the Planar QCD Loop Equation via a Matrix Ensemble
Alexander Migdal
We construct an exact solution to the planar QCD loop equation in four-dimensional Euclidean space using a novel matrix-valued momentum loop formalism. Central to this construction…