It is shown that the Chern–Simons functional, built in the spinor representation from the initial data on spacelike hypersurfaces, is invariant with respect to infinitesimal conformal rescalings if and only if the vacuum Einstein equations are satisfied. As a consequence, we show that in the phase space the Hamiltonian constraint of vacuum general relativity is the Poisson bracket of the imagin...

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric YangMills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of t...

By computing anomalous dimensions of gauge invariant composite operators (ψ̄ψ) and (φφ) in Chern-Simons fermion and boson models, we address that Chern-Simons interactions make these operators more relevant or less irrelevant in the low energy region. We obtain a critical Chern-Simons fermion coupling, 1 κ2c = 6 19 , for a phase transition at which the leading irrelevant four-fermion operator (ψ̄...

Let f be a boolean function. Define the circuit complexity of . . . No, wait! Let’s back up a little bit. Let me tell you how we ended up here. We are in Berkeley, California, in a circular-shaped building on the university campus. It is week five in the life of the Simons Institute for the Theory of Computation. This institute is named after James Harris Simons, an American mathematician who s...

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initi...

Using a geometric definition for the lattice Chern-Simons term in even dimensions, we have studied the distribution of Chern-Simons numbers for the 2d-U(1) and the 4d-SU(2) lattice Higgs models. The periodic structure of the distributions is preserved in our lattice formulation and has been examined in detail. In both cases the finite size effects visible in the distribution of Chern-Simons num...

We have studied the chiral phase transition in three-dimensional QED in the presence of a Chern–Simons term for the gauge field. There exists a phase where the chiral symmetry is broken dynamically and we have determined the critical line for this symmetry breaking as a function of the effective coupling and the strength of the additional Chern–Simons term. In the presence of a Chern–Simons ter...

We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle F LM −→ LM over the loop space of a Riemannian manifold M. Chern-Simons forms are defined roughly as in finite dimensions with the invariant polynomials replaced by appropriate Wodzicki residues. This produces odd dimensional R/Z-valued cohomolog...