TY - JOUR

T1 - 2 + 1 dimensional gravity as an exactly soluble system

AU - Witten, Edward

N1 - Funding Information:
*Research supported in part by NSF grant nos. 86-16129, 86-20266. * For various investigations of this problem from different viewpoints, see refs. \[1-8\].

PY - 1988/12/19

Y1 - 1988/12/19

N2 - By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.

AB - By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.

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U2 - 10.1016/0550-3213(88)90143-5

DO - 10.1016/0550-3213(88)90143-5

M3 - Article

AN - SCOPUS:33744722968

SN - 0550-3213

VL - 311

SP - 46

EP - 78

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -