Gauged Heterotic Sigma-models

The gauging of isometries in general sigma-models which include fermionic terms which represent the interaction of strings with background Yang-Mills fields is considered. Gauging is possible only if certain obstructions are absent. The quantum gauge anomaly is discussed, and the (1,0) supersymmetric generalisation of the gauged action given. Non-linear sigma-models are important two-dimensional field theories and those that are conformally invariant describe the propagation of a string in a curved space-time [1]. Gauging such sigma-models can give a construction of new conformal field theories, and gauged Wess-Zumino-Witten models provide a lagrangian formulation of the coset construction [2] . More recently, duality symmetry in string theory has been formulated in terms of gauged sigma-models [3], and this has led to the proposal of non-abelian generalisatons of duality symmetry [4]. Supersymmetric gauged sigma-models have also been used to construct (p,q) supersymmetric integrable models [5]. In [6,7,8], the gauging of general non-linear sigma-models with Wess-Zumino terms was shown to be possible only if certain obstructions were absent, and the gauged action was given. The (p,q) supersymmetric generalisations of these sigma-models were constructed in [9]. The purpose of this paper is to extend these results to the case of sigma-models with fermionic terms, representing the interaction of strings with background Yang-Mills fields C i , in addition to the metric gij , anti-symmetric tensor gauge field bij and dilaton Φ. In particular, the (1,0) supersymmetric version of such terms describes the propagation of heterotic strings in backgrounds with non-trivial gauge fields [10] and the gauged version can be used to formulate the effect of duality transformations on Yang-Mills fields [12]. The action for a bosonic two dimensional sigma-model with Wess-Zumino term and Fradkin-Tseytlin term is S0 = 1 2 ∫ dx √ h ( gij∂ φ∂μφ j + ǫbij∂μφ ∂νφ j + ΦR ) (1) where the D-dimensional target space M has metric gij(φ), coordinates φ i (i = 1, ...D) and torsion three-formH given in terms of a potential bij byHijk = 3 2∂[ibjk]. It is invariant under the transformation δφ = eλξ a (2) where λ (a = 1, ...n) are infinitesimal constant parameters, e is a constant and ξa