Quantum energy inequalities and their implications in semiclassical gravity

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In general relativity, energy conditions (ECs) are restrictions imposed on the stress-energy tensor to encode physically reasonable constraints on matter such as the positivity of mass. ECs play a critical role in understanding the structure of spacetime. Despite their widespread use, pointwise ECs do not generally hold. In particular quantum field theory (QFT) violates classical pointwise ECs due to the existence of negative energy states. Quantum energy inequalities (QEIs) have been derived to constrain the accumulation of negative energy. While QEIs have been broadly established in QFTs, there is no general result for self-interacting theories.The goal of my PhD is to contribute to the development of QEIs in interacting QFTs and their application to semiclassical gravity. This report summarizes my work towards that goal during the first year of my PhD. In collaborative work, we have described non-minimal coupling to gravity as an effective field theory in which the field value is controlled by the theory's cutoff. This allowed us to show that the null energy averaged over a region of spacetime obeys a state dependent bound. Additionally, we have studied null energy in $d$-dimensional CFTs. We explored the possibility of large negative null energy in the class of states defined by the action of the stress-energy tensor on the vacuum. While negative energy is possible, we haven't found null energy of the order of the central charge for an analysis based on the large-N factorization.