Spectral function sum rules from current algebra, unitarity and analyticity

Quantum gravity constraints from unitarity and analyticity

We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In D ≥ 4 spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in D 1⁄4 4 and D 1⁄4 5 before extending to D ≥ 6. Afterwards, we derive positivity ...

Sum Rules from the Algebra of Fields

Spectral Sum Rules and Selberg's Integral Formula

Using Selberg's integral formula we derive all Leutwyler-Smilga type sum rules for one and two flavors, and for each of the three chiral random matrix ensembles. In agreement with arguments from effective field theory, all sum rules for N f = 1 coincide for the three ensembles. The connection between spectral correlations and the low-energy effective partition function is discussed.

Duality violations and spectral sum rules

We study the issue of duality violations in the V V −AA vacuum polarization function in the chiral limit. This is done with the help of a model with an expansion in inverse powers of the number of colors, Nc, allowing us to consider resonances with a finite width. Due to these duality violations, the Operator Product Expansion (OPE) and the moments of the spectral function (e.g. the Weinberg su...

Electromagnetic Emission Rates and Spectral Sum Rules ∗

The electromagnetic emission rates at SPS energies satisfy spectral constraints in leading order in the pion and nucleon densities. These constraints follow from the strictures of broken chiral symmetry. We saturate these constraints using available data, leading to model independent emission rates from a hadronic gas. With a simple fire-ball scenario, only large nucleon densities may account f...