Solving field equations in non-isometric coset CFT backgrounds

The largest known class of gravitational backgrounds with an exact string theoretical description is based on coset G/HG/H CFTs and the corresponding gauged WZW models. These backgrounds generically lack isometries and are quite complicated. Thus the corresponding field equations seem impossible to solve and their use in physical applications becomes problematic. We develop a systematic general method enabling us to overcome this problem using group theory. The method is inspired by observations made in some elementary geometric coset and coset CFTs, but its full power is apparent in non-abelian cases. We analyze exhaustively the coset SU(2)×SU(2)/SU(2)SU(2)×SU(2)/SU(2) and explicitly solve the scalar wave equation of the corresponding gravitational background. We also examine the high spin limit and derive the effective geometry that consistently captures the corresponding sector in the theory.