Krishnamurthy obtained his BSc (Hons) in Physics (1970) from Bangalore University and MSc (Physics) (1972) from IIT, Kanpur. He studied in Cornell University (1972–76) as an IBM fellow, working with Kenneth G. Wilson and John W. Wilkins. In his PhD thesis, he extended Wilson's numerical renormalization group solution for the Kondo problem to the symmetric Anderson impurity model. The extension to the asymmetric case was completed during his post-doctoral tenure (1976–78) at the University of Illinois. Krishnamurthy returned to India and joined the Department of Physics, IISc, Bangalore (1978) and became a Professor (1996). He has held sabbatical positions at Princeton University, Harvard University, Ohio State University, University of Cincinnati, UC Davis and Georgetown University.