NS5-brane backgrounds and coset CFT partition functions

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.