Speaker
Description
We provide a detailed review and extension of compact, exactly solvable, pure Abelian and non-Abelian gauge theories in 1+1 dimensions, which have many similarities to (3+1)D pure Yang-Mills like confinement and a theta term. We focus on the U(1), SU(N) and SU(N)/ZN gauge groups. For the Abelian (1+1)D QED theory, we present a non-relativistic quantum mechanics calculation of the electric dipole moment (EDM) for neutral bound states of heavy quarks, which is shown to diverge as the vacuum angle θ approaches π, marking a deconfinement transition. This characterizes a "Strong C/P Problem" in (1+1)D, where the EDM is T-even but C- and P-odd. We provide exact analytic expressions for the partition function and Wilson loops (showing area law) with full θ dependence, which could serve as a useful check for lattice and quantum simulations with the sign problem. Using the modular inversion property of Jacobi theta functions (Poisson summation), we map the sum over energy eigenvalues in the canonical formulation of the partition function to a sum over topological instanton sectors. The partition function is seen going to zero in the strong coupling limit when θ = π, as expected.
In the non-Abelian sector, explicit analytic partition functions on a torus for SU(N=2,3) are already known and the Hilbert space of SU(N)/ZN theories decomposes into N sectors characterized by different weightings of the second Stiefel-Whitney class. As ongoing work, we are attempting to reinterpret these partition functions from the perspective of 1/N "fractional instantons" that cannot be lifted to the universal enveloping group SU(N), and we do so by studying all incontractible loops in the moduli space of flat connections (i.e. the maximal torus quotiented by the Weyl group).