+ a_4 t^2+ ...\bigg)~.$$ Departures from the flat space limit are encoded in the two derivative correction $a_2$ proportional to the Ricci scalar and the four derivative correction $a_4$ that is a linear combination of Riemann squared, Ricci squared, and Ricci scalar squared.[^2]

We divide the one loop effective action (\[eq:Wdef\]) into divergent contributions $$\label{eq:Wdiv}
W_{\textrm{div}} =  \frac{1}{32\pi^2} \left( - {1\over 2\epsilon^4} - a_2 {1\over\epsilon^2} + a_4 \ln \epsilon^2\right) \textrm{Vol}_{\textrm{AdS}_4}~,$$ and a remainder that is finite. From either piece we can form the trace of the energy momentum tensor $$T^{\mu}_{\mu} = \frac{2}{\sqrt{-g}}g^{\mu\nu}\frac{\delta W}{\delta g^{\mu\nu}}~.$$ The logarithmic divergence of the effective action (\[eq:Wdiv\]) gives an anomalous contribution that is conventionally presented as $$\label{eq:acdef}
\langle T_\mu^\mu \rangle_{\rm an}= \frac{1}{(4\pi)^2} a_4 = \frac{1}{(4\pi)^2} \left( c W^2 - a E_4\right)~.$$ In the nonconformal theories we consider there may be additional contributions to the trace of the energy momentum tensor.

The values of $c$ and $a$ have been computed perturbatively by many researchers using different methods and schemes [@Christensen:1978md; @Eguchi:1980jx; @Birrell:1982; @Vassilevich:2003xt]. The values that are now standard (up to caveats discussed later in this section) are summarized in table \[table:centralcharges\] below.

        **Field**                $c$                  $a$                 $c-a$
  ---------------------- -------------------- -------------------- --------------------
       Real Scalar         $\frac{1}{120}$      $\frac{1}{360}$      $\frac{1}{180}$
       