TY - JOUR

T1 - On the structure of the topological phase of two-dimensional gravity

AU - Witten, Edward

N1 - Funding Information:
* Research supported in part by NSF Grant 86-20266 and NSF Waterman Grant 88-17521 .

PY - 1990

Y1 - 1990

N2 - The topological phase of two-dimensional gravity is re-examined. The correlation functions of the naturally occuring operators in the minimal topological model are computed, using topological methods, in genus zero and genus one. The genus-zero results agree with recent results obtained in exact solutions of "matrix models", suggesting that the two approaches to two-dimensional gravity are equivalent. The coupling of two-dimensional topological gravity to topological sigma models is investigated. The CP1 model appears to be almost as simple as the pure topological gravity theory. General, model-independent properties of the correlation functions are obtained which hold in coupling to arbitrary topological field theories and can serve as a qualitative definition of the topological phase of two-dimensional gravity. A number of facts that are familiar in the usual phase of string theory, such as the relation between vanishing of the canonical line bundle of a Kähler manifold and scale invariance of the corresponding field theory, have simpler echoes in the topological phase.

AB - The topological phase of two-dimensional gravity is re-examined. The correlation functions of the naturally occuring operators in the minimal topological model are computed, using topological methods, in genus zero and genus one. The genus-zero results agree with recent results obtained in exact solutions of "matrix models", suggesting that the two approaches to two-dimensional gravity are equivalent. The coupling of two-dimensional topological gravity to topological sigma models is investigated. The CP1 model appears to be almost as simple as the pure topological gravity theory. General, model-independent properties of the correlation functions are obtained which hold in coupling to arbitrary topological field theories and can serve as a qualitative definition of the topological phase of two-dimensional gravity. A number of facts that are familiar in the usual phase of string theory, such as the relation between vanishing of the canonical line bundle of a Kähler manifold and scale invariance of the corresponding field theory, have simpler echoes in the topological phase.

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U2 - 10.1016/0550-3213(90)90449-N

DO - 10.1016/0550-3213(90)90449-N

M3 - Article

AN - SCOPUS:0009243741

SN - 0550-3213

VL - 340

SP - 281

EP - 332

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2-3

ER -