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We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairsof Seiberg-dual gauge theories within string theory. The N=1 gauge theorieswith flavour are realized as low energy limits of the worldvolume theories onD-branes in unoriented non-critical superstring backgrounds. These unorientedbackgrounds are obtained by constructing exact crosscap states in theSL(2,R)/U(1) coset conformal field theory using the modular bootstrap method.Seiberg duality is understood by studying the behaviour of the boundary andcrosscap states under monodromy in the closed string parameter space.Comment: 23 pages, 2 figure

D-branes in unoriented non-critical strings and duality in SO(N) and Sp(N) gauge theories