TY - JOUR
T1 - Conformal field theory, two-dimensional quantum gravity and quantization of Teichmüller space
AU - Verlinde, Herman
N1 - Funding Information:
Research supported by NSF Grant PHY-80-19754. Bitnet address: hlv6Ei~pupthy.princeton.edu.
PY - 1990/6/25
Y1 - 1990/6/25
N2 - We formulate the geometric quantization of Teichmüller space by using its relation with SL(2, R) Chern-Simons gauge theory and show that the physical state conditions arising in this formalism are equivalent to the Virasoro Ward identities satisfied by the conformal blocks in CFT. We further show that transition amplitudes between the physical states of this quantum system have a direct correspondence with covariant amplitudes of two-dimensional induced quantum gravity. Possible applications of these results to Virasoro modular geometry and (2 + 1)-dimensional quantum gravity are indicated.
AB - We formulate the geometric quantization of Teichmüller space by using its relation with SL(2, R) Chern-Simons gauge theory and show that the physical state conditions arising in this formalism are equivalent to the Virasoro Ward identities satisfied by the conformal blocks in CFT. We further show that transition amplitudes between the physical states of this quantum system have a direct correspondence with covariant amplitudes of two-dimensional induced quantum gravity. Possible applications of these results to Virasoro modular geometry and (2 + 1)-dimensional quantum gravity are indicated.
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U2 - 10.1016/0550-3213(90)90510-K
DO - 10.1016/0550-3213(90)90510-K
M3 - Article
AN - SCOPUS:0000908438
SN - 0550-3213
VL - 337
SP - 652
EP - 680
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 3
ER -