We establish reflection positivity for Gibbs trace states defined by a certain class of Hamiltonians that describe the interaction of Majoranas on a lattice. These Hamiltonians may include many-body interactions, as long as the signs of the associated coupling constants satisfy certain restrictions. We show that reflection positivity holds on an even subalgebra of Majoranas.

A coupling of two distributions PX and PY is a joint distribution PXY with marginal distributions equal to PX and PY . Given marginals PX and PY and a real-valued function f(PXY ) of the joint distribution PXY , what is its minimum over all couplings PXY of PX and PY ? We study the asymptotics of such coupling problems with different f ’s. These include the maximal coupling, minimum distance co...

Model coupling is a nontrivial task that is not adequately supported in existing frameworks. Our long-term goal is to support the fast-prototyping of model couplings, enabling scientists to quickly experiment with a variety of linkings without having to make an upfront investment in reprogramming. The centerpiece of our framework, the Potential Coupling Interface (PCI), must expose all the char...

Global symmetries are expected to be violated by gravity, which may cause a serious problem models based on these symmetries. A famous example is the Peccei-Quinn solution strong CP in QCD axion models; it requires global U(1) symmetry respected with high quality, and even Planck-scale suppressed operators that violate would spoil this solution. Indeed, known gravitational instantons do break i...