I shall discuss an ongoing work which aims to investigate the issue of scale vs conformal invariance in the context of AdS/CFT. We consider the most general 4 derivative effective field theories involving gravity and a scalar field in AdS. We show that this theory admits a solution which breaks the full conformal invariance to just Poincare and scaling. However, it does not have the correct 2 point function and anomaly consistent with just having scale but no conformal invariance in the theory. We next compare the theory to Horndeski gravity with scalar. This theory also admits a solution having scale but no conformal invariance. Moreover, it has proper 2 point function and anomalies expected in such a theory. However, this leads to a puzzle since we can map our theory to Horndeski theory by a field redefinition.
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Meeting ID: 880 9276 6911