Abstract
This dissertation is a summary of investigations in two different branches of physics - a) theoretical high-energy physics and b) climate dynamics.
In the first part of this thesis, we will study the properties of entanglement entropy and R ́enyi entropies in Quantum Field Theories (QFTs). We begin our exploration by studying spatial entanglement in an interacting QFT. We consider the reduced density matrix for a disc in the ground state of the interacting fixed points of the large-N O(N) vector model in 2 + 1 dimensions. Using the map to the free energy on H2 × S1, we show that there is an instability in the R ́enyi entropies at n = 1, in the N → ∞ limit, indicating a phase transition at or near this R ́enyi parameter. However, we argue that this does not invalidate the replica trick, which is often used to obtain entanglement entropies from R ́enyi entropies.
In the second half of the first part, we study target space entanglement in gauged multi- matrix models as models of entanglement between groups of D-branes separated by a planar entangling surface, paying close attention to the implementation of gauge invariance. Along the way, we review the example of target space entanglement between identical particles, which shares some important features (specifically a gauged permutation symmetry) with our main problem. For our matrix models, we implement a gauge fixing well-adapted to the entangling surface. In this gauge, we map the matrix model problem to that of entanglement of a U(1) gauge theory on a complete or all-to-all lattice. Matrix elements corresponding to
open strings stretching across the entangling surface in the target space lead to interesting contributions to the entanglement entropy.
The second part of this dissertation is an attempt to develop a new bias-correction tech- nique for daily maximum temperature. The method called Quantile delta mapping (QDM), which is often used to map the present-day observed PDF of some variable (e.g., daily max- imum temperature) to a projected future PDF using the changes in quantiles from a global climate model (GCM), suffers from the problem of quantile crossing, which produces fu- ture quantile functions that are ill-defined because they are non-monotonic. We explore the alternative method of moment delta mapping (MDM), which, in application to daily maxi- mum temperature, has the bias-correction benefits of QDM, but never suffers from quantile crossing. We demonstrate the accuracy of MDM using daily maximum temperatures from 100 members of the Community Earth System Model 2 (CESM2) Large Ensemble (LENS2) spanning 150 years of simulation output.