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The effective actions for $d=2$, $N=3,4$ chiral supergravities with a linearand a non-linear gauge algebra are related to each other by a quantumreduction, the latter is obtained from the former by putting quantum currentsequal to zero. This implies that the renormalisation factors for the quantumactions are identical.Comment: 14 pages, LaTeX, LBL-323778, UCB-PTH-93/07, KUL-TF-93/1

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Relation between linear and nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mn>4</mml:mn></mml:math>supergravity theories

Relation between linear and nonlinearN=3, 4supergravity theories