Some nonabelian toy models in the largeN limit

Schwinger-Dyson equations are used to study the largeN limit ofU(N) gauge theory on several small lattices. Explicit solutions are found which are beyond the reach of existing steepest descent technique. They show a phase transition in a three placquette model at couplingg ² N=3, resembling the known transition in the one placquette model, and lending support to expectations of a similar transition in the four dimensional lattice theory.This work was supported in part by the High Energy Physics Division of the U.S. Department of Energy under contract No. W-7495-ENG-48     

Details of the non-unitarity proof for highest weight representations of the Virasoro algebra

We give an exposition of the details of the proof that all highest weight representations of the Virasoro algebra forc<1 which are not in the discrete series are non-unitary.This work was supported in part by DOE grant DE-FG02-84ER-45144, NSF grant PHY-8451285 and the Sloan Foundation     

Supersymmetric derivation of the Atiyah-Singer index and the chiral anomaly

We present an elementary derivation of the Atiyah-Singer formula for the index of the Dirac operator. This index is the space-time integral of the trace of the chiral anomaly. We calculate the full chiral anomaly using the supersymmetric path integral for a spinning particle moving through space-time.     

A proof of the Nielsen-Ninomiya theorem

The Nielsen-Ninomiya theorem asserts the impossibility of constructing lattice models of non-selfinteracting chiral fermions. A new proof is given here. This proof fills a technical gap in the two proofs presented by the authors of the theorem. It also serves as prelude to an investigation of the chiral properties of the general lattice model.     

Entropy Flow Through Near-Critical Quantum Junctions

Journal of Statistical Physics - This is the continuation of Friedan (J Stat Phys, 2017. doi: 10.1007/s10955-017-1752-8 ). Elementary formulas are derived for the flow of entropy through a circuit...     

Boundary entropy of one-dimensional quantum systems at low temperature

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the "ground-state degeneracy," g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.     

Entropy Flow in Near-Critical Quantum Circuits

Journal of Statistical Physics - Near-critical quantum circuits close to equilibrium are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective...