Memories, asymptotic symmetries, and soft theorems

Last Monday, the Strings 2015 annual conference started in Bengalúru, India. Now it's over. With three exceptions, the written documents used by the speakers are posted on the page with talk titles and videos. Unfortunately, most of the videos have still not been posted; the last released ones were added 4 days ago.

(Update July 1st: thank God, the videos are available.)

There have been numerous interesting talks at the conference. Some of them are nice reviews. In order to focus on talks with a truly new original content that is sufficiently conceptual to be appropriate for a semitechnical blog, let me pick Andy Strominger's talk (PDF), not only because Andy celebrates his 60th birthday in a month.




Like other Strominger PDF files, you find lots of cute childish drawings inside, all of which could have been contributed by one of his daughters.




Andy was reporting on the content of 12 papers he co-wrote since August 2013 along with 9 collaborators, with contributions from 46+ other physicists he enumeartes at the beginning.



On Wednesday after the conference week, the video was finally posted, thank God.

Without a loss of generality, let us use the term Strominger-Pasterski et al. for this group of physicists. Sabrina Gonzalez Pasterski (physicsgirl.com) is a teenage pilot and one of 30 under 30 who has already attended the Lindau meeting of Nobel prize winners. ;-)



I am sure that if Tim Hunt posted this Sabrina 1988 music video about her collaborators and the distractions, he would be in hot water. ;-)

Most TRF readers are mature white men above 80 years of age. But those TRF readers who are teenagers and who want to work with Andy Strominger should know that you must first learn how to pilot an aircraft and build your aircraft before you are 17. Once you do that, you must meet the founder of Amazon.com who convinces you to do physics instead. (I am sure that once I describe her in this way, Andy Strominger feels even prouder that he could have collaborated with her.)

Strominger's slogan summarizing the 12 recent papers is a triangle linking all 3 pairs of three previously independent concepts:

1. gravitational memory
2. soft theorem
3. asymptotic symmetry

Black holes carry lots of entropy or information which we often imagine as something that resides in the ultrashort distance regime of quantum gravity. But Strominger-Pasterski et al. want to reimagine all these things from the viewpoint of very long distance physics, i.e. from the deeply infrared perspective.

You make operations at very long distances and the gravitational systems remember what you do; we are talking about operations involving the gravitational field's influence on rotating satellites, something that NASA and pals are actually going to test soon. OK, that's my very cheap sketch of the memory part.

The soft theorem is Weinberg's 1965 observation that the addition of a very soft graviton (one with a zero momentum) to an S-matrix scattering process only changes the S-matrix amplitude in an extremely simple way.

This law is a universal principle and similar principles may often be explained by symmetries. So Strominger-Pasterski et al. identify the symmetries – some new asymptotic symmetries. They are basically translations ("supertranslations" but not in the supersymmetric sense) where the displacement depends on the angle – or new Virasoro symmetries acting on the sphere at infinity. If you want just some extra details, the first newly found symmetries of the gravitational scattering arise as a diagonal subgroup of BMS⁺ x BMS^–, the pair of the asymptotic scri-plus-and-minus BMS supertranslation groups. This new symmetry is infinite-dimensional; the corresponding conservation laws are pretty much separate energy-like conservation laws for each direction in the two-sphere at null infinity.

If we return to the triangle, it works just like rock-paper-scissors. The new asymptotic symmetries explain the soft theorem, as a special case of the Ward theorem; the soft theorem produces memory through the Fourier transform; and memory implies asymptotic symmetries if you consider vacuum-vacuum translations.

I am afraid that you will have to read at least some of those 12 papers (or at least look at the talk) to understand what Strominger-Pasterski et al. actually mean. But the overall message is that there are richer insights and structures hiding (and partially waiting to be understood) in the deeply infrared (long distance) behavior of the quantum gravitational theories. Three more specific conclusions described in Andy's talk:

1. black holes carry an infinite amount of BMS hair (Burg, Metzner, Sachs 1962 supertranslations i.e. certain diffeomorphisms defined through their simple action on radiative data at scri-plus)
2. the Hawking radiation is constrained by an infinite tower of related conservation laws
3. the zero-energy vacuum boasts an infinite degeneracy i.e. it can store an infinite amount of information

The mysteries of quantum gravity don't necessarily hide in the ultrashort phenomena that may only be seen with the impossible Planckian eyeglasses. Using some better tools to look at them, a big part of the information about those mysteries may be projected at infinitely long distances. The temperature of the Hawking radiation isn't the only "parameter" that describes it; even if you only allow long-distance apparatuses, lots of additional hair and information is encoded in the charges under those supertranslations etc.

This summary was distilled from my incomplete technical understanding what all those 12 papers are doing but my guess is that Strominger would largely agree, anyway.