Graph theory and the Virasoro master equation

Technical Report · Mon Apr 01 00:00:00 EST 1991

OSTI ID:5501893

Obers, N A.J.

A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equations is given. By studying ansaetze of the master equation, we obtain exact solutions and gain insight in the structure of large slices of affine-Virasoro space. We find an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabelled graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. We also define a class of magic'' Lie group bases in which the Virasoro master equation admits a simple metric ansatz (gmetric), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, we define the sine-area graphs'' of SU(n), which label the conformal field theories of SU(n){sub metric}, and we note that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}. 24 figs., 4 tabs.

• Research Organization: Lawrence Berkeley Lab., CA (United States)
• Sponsoring Organization: USDOE; USDOE, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5501893
• Report Number(s): LBL-30634; UCB-PTH-91/24; ON: DE91016432; CNN: PHY90-21139; PHY85-15857
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

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