| dcterms.abstract | Conformal eld theory (CFT), especially two dimensional conformal eld theory, has been an active and fruitful topic of theoretical physics for decades. As a powerful tool and insightful approximation, it has been widely used in dierent elds of physics such as string theory, statistical physics, and condensed matter physics. In this dissertation I shall discuss two dierent subjects in which the results of 2D CFT can be applied: entanglement negativity and the soft gluon/graviton theorem. 2D CFT is one of the most important approaches in calculating entanglement of 1D free systems. By applying the replica trick, the entanglement entropy can be expressed as the path integral of the free eld on a Riemann surface, or equivalently as correlation functions of corresponding twist operators. The same approach applies to negativity, a well dened measure of entanglement for mixed states. In this dissertation, we discuss the negativity of free fermions, which is a hard problem because individual terms in the sum over spin structures do not respect the replica symmetry. I shall present in detail how some of the terms can be reduced to rational functions by Thomae's formula and how to use these terms to construct upper and lower bounds on free fermion negativity. In the second part of the dissertation, I shall discuss the soft gluon/graviton theorem of scattering amplitudes. The connection between 4D scattering amplitudes and 2D CFT has been discussed at length in recent years. They share the same SL(2;C) symmetry. By replacing the plane wave external legs with an SL(2;C) wave packet, one can transform from scattering amplitudes to Witten diagrams in AdS3, which then map to correlation functions on the boundary. The soft gluon and graviton theorems can then be re-expressed as Ward identities of the BMS symmetry. In this dissertation, I shall show how these two soft theorems are related through KLT relations. | |
