Every good drama student knows about the world on which Nora Helmer slammed the door when she walked out of ''A Doll's House,'' the famous Henrik Ibsen domestic drama. To find herself, Nora abandoned her devoted but patronizing husband, her three children, and an imprisoning domesticity she could no longer endure.
More than a century after the Ibsen play first appeared, the librettist-lyricist team of Betty Comden and Adolph Green have audaciously imagined what befell Nora after the final curtain. Their speculations, entitled ''A Doll's Life,'' take the form of a Broadway musical romance, for which Larry Grossman has written the score. The production, staged with customary precision and finesse by Harold Prince, stars Betsy Joslyn as the truant Nora. It also stars George Hearn in three roles: an actor playing Torvald Helmer; Torvald himself; and Johan, Nora's sometime protector in the bewildering metropolis of Christiania.
''A Doll's Life,'' at the Mark Hellinger Theatre, begins as a group of present-day actors rehearsing the final scene of Ibsen's play. Miss Joslyn's Nora, upset by some sharp comments from Mr. Hearn's actor-director, quits the set and segues into the abstract and hypothetical world of Comden-Green imaginings. It is a world whose scenic visualizations (by Timothy O'Brien and Tazeena Firth) recall the dark colors and intensities of Edvard Munch paintings. For further atmospheric touches, choreographer Larry Fuller's fleeting dance patterns are executed by figures from Munch canvases. Ken Billington provided the lights and shadows.
Rather than going forward from Ibsen, ''A Doll's Life'' resembles the kind of synthetic stage fiction against which the great Norwegian was rebelling. In a series of brief scenes, with songs and Florence Klotz costumes to match, Nora pursues her adult education. She is successively waitress, wardrobe assistant at the opera, cannery worker, women's rights activist (for which she is briefly imprisoned), and mistress-adventurist. In the course of these experiences she discovers the power of money and makes enough of it to become independent. The finale of this old-fashioned scenario is neither more nor less improbable or ludicrous than anything that has gone before. It is simply rather a long time arriving.
''A Doll's Life'' has been assembled by a creative team trailing credits and awards. Why, with a reported investment of $4 million, they have not been able to bring off something more engaging and entertaining is one of the mysteries of show business.
The Grossman score is frequently attractive and is admirably performed throughout by Miss Joslyn, a pert, pretty, 20th-century Nora; by Mr. Hearn in whatever guise; and by their colleagues in a large and splendid cast. The principals include Edmund Lyndeck as a ruthless capitalist and Peter Gallagher as an aspiring composer. Members of the ensemble fill multiple roles. Paul Gemignani directed the musical performance and Bill Byers orchestrated the score.
''A Doll's Life'' flirts along the way with opera lampoon in the interpolated background scenes of a pastiche entitled ''Loki and Baldur,'' a Norwegian saga set to music. It prompted wistful recollections of Comden and Green doing ''Carried Away'' and Mr. Green as a wildly ferocious Captain Hook. There is nothing nearly so exhilarating in ''A Doll's Life.''