SYMMETRY REORGANIZATION IN EXACTLY SOLVABLE TWO-DIMENSIONAL QUANTIZED SUPERGRAVITY

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Abstract
A recent work of Polyakov solving exactly the two-dimensional induced quantum gravity is extended to the two-dimensional induced (1,0) quantum supergravity theory. This theory is found to be exactly integrable in a supersymmetric version of the light cone gauge. Solutions are found to display an infinite dimensional Z2 graded sl(2, R) invariance and a diffeomorphism invariance in one of the coordinates. The origin of these invariances is traced to motions along the gauge slice. A Sugawara construction based on the currents of the infinite dimensional transformations is shown to generate these diffeomorphisms. Explicit results are given for a number of quantum correlation functions.

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