On December 1, Alex Sandomirsky successfully defended the thesis, “Explicit Conformal Blocks” (advisor: Witold Skiba).
Sandomirsky explained, “Conformal field theories (CFTs) are theories in which the laws of physics don’t care about the overall scale of the coordinate system you’re using. The nature of these highly symmetric theories is important for our understanding of critical phase transitions as well as the low and high energy behaviors of general particle theories. My work deals with how imposing this symmetry constrains the possible range of interactions in a theory. Specifically, we constructed conformal blocks, which are technical objects that appear in consistency equations, which then restrict a CFT’s dynamics.”
His next position will be as a quantitative researcher at Midpoint Markets.
Thesis Abstract:
Conformal field theories (CFTs) are important in their application to critical phenomena, as fixed points in the renormalization group of QFTs, and with their role in the AdS-CFT correspondence. The conformal bootstrap has been a useful tool in carving out the space of allowed CFTs and relies on the computation of four point conformal blocks. Currently, a few specific examples for certain spin configurations are worked out in the literature; I set out to obtain general and explicit expressions for these blocks in three and four dimensions, for arbitrary spins. This is accomplished by working in the embedding space formalism of CFTs, deriving projection operators for irreducible representations of the Lorentz group, and enumerating the independent tensor structures that behave as these representations.