Infrared triangle

The infrared triangle is an equivalence relation which is proposed to govern the longwave energy, or infrared, dynamics of all physical theories involving massless particles. The relation was proposed in a series of lectures on soft theorems in quantum field theory, gravitational memory effects, the Bondi–Metzner–Sachs group, non-abelian gauge theory, and gravity related to black holes by Andrew Strominger in 2016.^[1]

The relation identifies a single underlying structure that connects infrared behavior in gravity and quantum field theory. It shows that a physical effect, a spacetime symmetry, and a quantum scattering rule are mathematically equivalent, so that understanding any one of them reveals the content of the others.^[2]

The three corners of this triangle are:

• memory effects, which is the lasting displacement left in spacetime after a gravitational wave has passed;
• supertranslation symmetries, which are an infinite set of transformations that empty spacetime satisfies; and
• soft particle theorems, which govern the behavior of particles with nearly zero energy.

This implies there may be a measurable memory signal provides evidence for these symmetries and quantum relations, giving a unified view of infrared dynamics and helping to constrain possible theories of quantum gravity.^[2]