Níck

theoretical physicist

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Infrared Structure

While the ultraviolet behavior of quantum field theories was tamed by the renormalization program, the infrared structure was for a long time considered to be trivial and uninteresting. Nowadays, we understand there is extremely rich physics at long distances and low frequencies. This has sparked a lot of interest in many subareas of fundamental physics.

Firstly one has the so-called Bondi–Metzner–Sachs Group (BMS) group, which is the symmetry group at null infinity of asymptotically flat spacetimes. In principle, one would expect this group to be simply the Poincaré group, since asymptotically flat spacetimes should resemble Minkowski spacetime at infinity. Nevertheless, the correct Lie group is infinite-dimensional, being comprised of the Poincaré transformations and the so-called supertranslations, which are direction-dependent translations. This means general relativity does not reduce to special relativity at very large distances, but rather to something much more complicated. The existence of this infinite-dimensional symmetry group at the boundary of the spacetime can be exploited to obtain more information about what happens in the bulk.

Secondly one has Weinberg’s soft graviton theorem. A soft particle is a particle with very small energy. Weinberg’s soft graviton theorem relates a scattering amplitude to the amplitude for the same scattering process with the addition of a number of soft gravitons. This turns out to be a consequence of the BMS symmetries at null infinity, and it is fundamental to fully understand scattering in quantum field theories involving gravitons or gauge fields.

Thirdly, one has the gravitational wave displacement memory effect. This is the prediction that two nearby inertial detectors close to infinity will be permanently displaced by the passage of a gravitational wave. The computations involved in the prediction of this effect can be matched to the soft graviton theorem, and the effect can be understood as a physical realization of a BMS translation. This prediction is expected to be measured in future gravitational wave detectors.

The connections between these three topics allow one to study one of them to gather information about the other two, leading into further insights on the behavior of quantum gravity at very low energies.

Some modern applications of these ideas include

  • celestial holography: the pursuit of a holographic correspondence between quantum gravity in four-dimensional asymptotically flat spacetimes and a conformal field theory on the two-dimensional sphere at infinity;
  • infrared finite scattering theory: appropriately describing the S-matrix for scattering in asymptotically flat spacetimes, while taking into consideration the difficulties caused by infrared divergences;
  • construction of Hadamard states: exploiting the BMS symmetries at infinity to define physically meaningful states for quantum field theories on asymptotically flat spacetimes.

Further Reading

The following references discuss different aspects and uses of the infrared structure of gravity and other field theories.

My Publications on and Around This Topic

  • Aguiar Alves, Níckolas de. 2025. “Lectures on the Bondi–Metzner–Sachs group and related topics in infrared physics.” arXiv: 2504.12521 [gr-qc]. Summarized here.
  • Aguiar Alves, Níckolas de, and André G. S. Landulfo. 2025. “The Sky as a Killing Horizon.” arXiv: 2504.12514 [gr-qc]. Summarized here.