Wilson–’t Hooft line operators as transfer matrices

Hausdorff Matrices as Bounded Operators over /

A necessary and sufficient condition is obtained for an arbitrary Hausdorff matrix to belong to B(l). It is then shown that every conservative quasi-Hausdorff matrix is of type M. Let (H, u) denote the Hausdorff method with generating sequence ¡x = {/L,}, / = {{xn} \2„\xn\ < oo}, B(l) the algebra of bounded linear operators on /. A necessary and sufficient condition is obtained for an arbitrary...

Wilson-’t Hooft operators and the theta angle

We consider (3+1)-dimensional SU(N)/ZN Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle θ → θ+2π, a ’t Hooft operator T (γ) associated with a closed spatial curve γ that winds around the compact direction undergoes a monodromy T (γ) → T (γ). The new ’t Hooft operator T (γ) transforms under large ga...

Spectral operators of matrices

The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool to model many important applications involving structured low rank matrices within and beyond the optimization community. This trend can be credited to some extent to the exciting developments in emerging fields such as compressed sensing. The Löwner operator, which generates a matrix valu...

The ’t Hooft Model As A Hologram

We consider the 3d dual of 1 + 1 dimensional large-Nc QCD with quarks in the fundamental representation, also known as the ’t Hooft model. ’t Hooft solved this model by deriving a Schrödinger equation for the wavefunction of a parton inside the meson. In the scale-invariant limit, we show how this equation is related by a transform to the equation of motion for a scalar field in AdS3. We thus f...

Generalized Hausdorff Matrices as Bounded Operators on ! p*