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Structure of dynamical Chern Simons gravity and higher derivative theories

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I discuss the partial differential equation structure of the dynamical Chern Simons (dCS) model of gravity (as time-evolution problem) and argue that this theory is not hyperbolic (and, therefore, not a well-posed initial value problem). The dCS model of gravity finds motivations in String Theory and Loop Quantum Gravity as an effective low energy model. It consists in adding the Pontryagin density coupled to a (dilaton-like) scalar field to the Einstein Hilbert Lagrangian. This introduces higher derivatives in the model which spoils its hyperbolic structure. Instead, I will argue that trading the Einstein-Hilbert term to the conformal gravity Lagrangian can in principle improve the situation by comparing the model to its electromagnetic counterpart. Finally, I will show that treating dCS gravity perturbatively as an effective theory is well behaved to all orders in the dCS coupling.

This talk is part of the DAMTP Friday GR Seminar series.

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