Muntean (IM): This is a case in which novelty in emergence is very obvious – the eisntein field equations are completely unexpected!
TV: Yes, it’s magic!
IM: But if we’re talking about Batterman and Butterfield’s approaches where’s the limit that we’re taking in the Polyakov action?
TV: Take a full expansion and then takes a low energy limit – but the emergence isn’t at this stage – this is just a matter of focussing attention on the lowest level of perturbation. The deduction of GR comes after we take the limit a la Butterfield. But she’s worried that she’s not really doing the right kind of deduction because it involves assumptions about conformal invariance which isn’t an intrinsic formal feature of the theory. If we think the conformal invariance condition is external, then we have a stronger emergence a la Batterman.
Pitts: If we’re integrating over the worldsheet in the action, how can we contract the metric – we have worldsheet indices running only from 1-2, so how do we get out vanishing of the whole Ricci tensor?
TZ: If we think about conformal invariance, then we do need vanishing of the Ricci tensor.