Pasterski–Strominger–Zhiboedov triangle

In theoretical physics, the Pasterski–Strominger–Zhiboedov (PSZ) triangle or infrared triangle is a series of relationships between three groups of concepts involving the theory of relativity, quantum field theory and quantum gravity. The triangle highlights connections already known or demonstrated by its authors, Sabrina Gonzalez Pasterski, Andrew Strominger and Alexander Zhiboedov.

The connections are among weak and lasting effects caused by the passage of gravitational or electromagnetic waves (memory effects), quantum field theorems on graviton and photon and geometrical symmetries of spacetime. Because all of this occurs under conditions of low energy, known as infrared in the language of physicists, it is also referred to as the infrared triangle.

Related concepts
The concepts that are interconnected by the triangle are:


 * a) soft particle theorems (quantum field theory theorems regarding the behavior of low-energy gravitons or photons):
 * soft graviton theorem, published by Steven Weinberg in 1965;
 * extension of the previous theorem, published by Freddy Cachazo and Strominger in 2014;
 * soft photon theorem, also published by Weinberg in the same paper of 1965 regarding the graviton;
 * b) asymptotic symmetries (symmetries of spacetime distant from the sources of the fields):
 * supertranslations of the Bondi-Metzner-Sachs group, published in 1962;
 * superrotations (symmetry analogous to that of the Virasoro algebra), published by Glenn Barnich and Cédric Troessaert in 2010;
 * symmetries of U(1) gauge theories, published by Pasterki in 2017;
 * c) memory effects:
 * gravitational memory effect, published by Yakov Zeldovich and A. G. Polnarev in 1974 and Demetrios Christodoulou in 1991;
 * new gravitational memory effects, published by Pasterski, Strominger and Zhiboedov in 2016;
 * the electromagnetic analogue of the memory effect, published by Lydia Bieri and David Garfinkle in 2013.

Binding relationships
Each group is linked to another by special relationships:


 * Fourier transforms tie together soft theorems and memory effects;
 * vacuum transitions tie together asymptotic symmetries and memory effects;
 * Ward's identities tie together soft theorems and asymptotic symmetries.

So, for example:


 * the soft graviton theorem (a.1) is related to the supertranslations (b.1) by a Ward's identity;
 * the supertranslations (b.1) correspond to different vacuum states created by the gravitational memory effect (c.1)
 * the gravitational memory effect (c.1) reduces to the soft graviton theorem (a.1) via a Fourier transform.

In addition to the first triangular relationship highlighted by the authors, several others may exist and have been hypothesized.