2 + 1 dimensional gravity as an exactly soluble system

1988/12/01 by Edward Witten · 2 voices · 336 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories

paper · doi:10.1016/0550-3213(88)90143-5

crossref issued 1988/12/01 · crossref published 1988/12/01 · crossref published-print 1988/12/01 · openalex publication_date 1988/12/01 · crossref created 2002/11/12 · crossref deposited 2025/09/10 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31

Citations

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Discussions

• This argument does not work. Let me recall why non-compact gauge group means no ground state. Yang-Mills, by definition, has lagrangian $$ L=K(F,F) $$ where $K$ is the Killing form on the algebra of t [stackexchange, 2 points]
• TL;DR: The Poincare algebra $\mathfrak{iso}(2,1)$ in 2+1D Minkowski spacetime $\mathbb{R}^{2,1}$ is an Inonu-Wigner contraction $\Lambda\to 0$ of the isometry Lie algebra $$\mathfrak{so}(3,1)\qquad\le [stackexchange, 2 points]