Nuclear Physics B362 (1991) 199-231 North-Holland LAGRANGIAN CHIRAL COSET CONSTRUCTION OF HETEROTIC STRING THEORIES IN (1, 0) SUPERSPACE S. James GATES, Jr.*'** and S.V. KETOV*** Department of Physics and Astronomy, University of Maryland at College Park, College Park, MD 20742-4111, USA S.M. KUZENKO and O.A. SOLOVIEV Tomsk State Unit~ersity, Lenin Ave. 36, Tomsk 634050, USSR Received 25 February 1991 We present invariant actions describing (1,0) supersymmetric non-abelian leftons and rightons on coset manifolds. Our discussion covers both chiral and non-chiral cases of the (1,0) supersymmetric WZNW actions. We analyze the supergravitational, chiral and Siegel anomalies of D < 10 heterotic strings within the lagrangian realization of GKO coset construction. General conditions for anomaly cancellation are found and various anomaly-free solutions are discussed. Among these are the "realistic" ones, such as the Gepner models and the four-dimensional heterotic strings compactified on orbifolds. Coupling of the heterotic string coset models to bosonic massless modes and the Siegel anomalies of the associated non-linear or-models are briefly considered. I. Introduction A development of geometrical covariant description for four-dimensional (4D) heterotic strings and manifest covariant realization of their internal and world-sheet symmetries can be achieved by the use of two-dimensional (2d) lagrangian field theory in a curved (1, 0) superspace. The very useful ingredients in this construc- tion are (1, 0) supersymmetric chiral bosons (leftons and rightons) and non-movers (notons). 4D heterotic strings have two standard descriptions with internal degrees of freedom to be represented by either chiral bosons or chiral fermions [1]. The 4D heterotic string in the free fermion approach [2,3] exists only in the superconfor- mal gauge and cannot be considered as the gauge-fixed form of a covariant action * Research supported in part by NSF grant PHY88-16001-A02. **Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA. ***On leave of absence from: High Current Electronics Institute of the USSR Academy of Sciences, Siberian Branch, Akademicheskii 4, Tomsk 634055, USSR. 0550-3213/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)