THE NOTEBOOKS OF XINGYANG YU / No. 01
Gravity,
in three
dimensions.
A universe without gravitational waves.
A black hole anyway.
And a question that refuses to go away.
An abstract illustration.
The waves disappear.
The mystery stays.
Take away one dimension of space and gravity loses its local waves. Yet boundaries carry states, black holes have entropy, and the quantum theory remains a remarkably demanding puzzle.
This is a route through the ideas that made the puzzle sharper. Read it in order, or begin with the surprise that catches your eye.
Follow the questions.
Organized by ideas, not decades.
A selected route, not an exhaustive history.
A universe without gravitational waves
Remove a dimension, and gravity loses its ripples. The interesting part is what refuses to disappear.
4 MIN 021986 · Brown–HenneauxThe edge has more to say
A transformation can be empty bookkeeping in the bulk and a physical operation at infinity.
4 MIN 031986–1988 · Achúcarro–Townsend and WittenWhen gravity became a gauge theory
A change of variables opens a new toolbox—and makes the meaning of “the same theory” unexpectedly delicate.
4 MIN 041992 · Bañados–Teitelboim–ZanelliThe black hole that was still there
No gravitational waves. Constant local curvature. And yet, an event horizon.
4 MIN 051986–1998 · Cardy, holography, and BTZ entropyCounting states you have not met
How symmetry gets the black-hole entropy right before we know the full microscopic story.
3 MIN 062007 · The extremal proposalHow empty can a quantum theory be?
Pure gravity suggests a sparse spectrum. Extremal CFT asks how far that ambition can be pushed.
4 MIN 072007–2010 · The Maloney–Witten calculationAdd up the geometries. Do you get a theory?
A gravitational path integral passes a symmetry test and runs into a state-counting problem.
4 MIN 082007–2010 · Higher genus and consistencyA second handle asks harder questions
A spectrum is a beginning. Sewing surfaces asks whether the pieces know how to work together.
4 MIN 092020–2022 · Wormholes and CFT statisticsOne theory—or many?
Wormholes invite a statistical interpretation. The hard part is specifying exactly what is random.
4 MIN 102023 · Virasoro TQFTA new machine for an old question
Virasoro TQFT turns gluing into a computational language. A full definition of gravity still asks for more.
4 MINNo stories match. Try another word.
Where the story opens up.
Three questions to carry beyond the last page.
When does a candidate become a theory?
A modular function is not yet a complete CFT. What data and consistency conditions are still missing?
Return to extremal CFT →02 / INTERPRETATIONWhat, exactly, is being averaged?
An ensemble of selected data and a probability measure over exact theories are different targets.
Follow the ensemble question →03 / DEFINITIONWhich amplitudes make a quantum gravity?
Fixed-topology calculations are powerful. A complete prescription must also say how they fit together.
Explore Virasoro TQFT →Understanding comes
before the next claim.
These essays follow a question from one useful observation to the next. The reading order is conceptual: several historical developments overlap, and the dates are signposts rather than chapter boundaries.
Written with AI assistance for Xingyang Yu’s gravity notebook. Sources are linked in every article. This first edition is explanatory writing, not a claim of new research results. Corrections are welcome.
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