Correlation Functions in the Bosonic Theory (Continuum Approach for Spherical Topology)

Abstract

AbstractTwo-dimensional gravity describes important phenomena11,43, such as random surfaces and string theories away from criticality. Up to recently, the most efficient means of extracting results from the theory of two-dimensional gravity was the matrix model approach56,70, to be discussed later. In this theory, one obtains a series expansion in the genus with determined coefficients. However, that theory suffers some drawbacks, such as difficulties in the interpretation of real solutions of the Painlevé equation70 in the light of the “Schwinger-Dyson” equations71, or the lack of a super matrix model formulation, due to the well known difficulty of defining lattice fermions, which is necessary to deal with two-dimensional supergravity. Therefore, alternative computations and their detailed comparison is mandatory in order that the correct points be settled. Thus, we use the zero mode integration technique for Liouville72–78 and super Liouville79–82 theory, in order to be able to compute correlators of dressed vertex operators in the continuum, as well as in the matrix model/KdV63,71,83 approach, or also with a super eigenvalue model84, to deal with the discrete theory in subsequent chapters.KeywordsPartition FunctionMatrix ModelVertex OperatorConformal DimensionDiscrete StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.