Suppose I have some Lagrangian of some higher derivative gravity coupled to a may be matter fields. Now I want to fluctuate it to quadratic order about an AdS background and calculate the 1-loop partition function.
Can someone point to a reference where such a thing might be done? This sounds like something standard which someone would have done...
I can't see how one can even write down the fluctuated Lagrangian to quadratic order...And even if I wrote that down, how does one impose that the background is AdS? Then the issues of gauge fixing and ghosts are only added complication..
I can imagine calculating the first order variation in the Christoffel symbols and Riemann and Ricci tensors but that goes only so far.