Tachyon condensation at one loop
  Using boundary string field theory we study the decay of unstable D-branes to lower dimensional D-branes via the tachyon condensation at one loop level. We analyze one loop divergences and use the Fischler-Susskind mechanism to cancel divergences arising at the boundary of moduli space. The tachyon action up to the second derivative is obtained and a logarithmic correction to the tachyon potential is written down explicitly. Multiple D-branes is also considered and the role of the boundary fermions is highlighted. 
D. Nemeschansky and V. Yasnov