Emergent Flattening of Moment-Curve-Like Geometries

Geometry, Symmetry and Physics
Event time: 
Monday, March 27, 2023 - 4:30pm
LOM 214
Aidan Herderschee
Speaker affiliation: 
University of Michigan
Event description: 

In this talk, I discuss how an infinite dimensional convex geometry of interest to physicists exhibits "flattening," which manifests as emergent equalities among naively independent coordinates. This flattening behavior is intrinsically tied to the infinite dimensional nature of the convex geometry, as these emergent equalities only appear in the infinite dimensional limit. In more detail, the space of causal and unitary theories, called the EFT-Hedron, is identified as the intersection of a convex region given by the Minkowski sum of two moment curves and a hyperplane in an infinite dimensional projective space. I use linear programming to provide strong numeric evidence that the EFT-hedron "flattens out." For example, restricting a finite fraction of the coordinates to be even-zeta values, the remaining coordinates are (conjecturally) fixed to take odd-zeta values. I will conclude by briefly sketching how this conjecture relates to Type-I superstring theory, which corresponds to a particular point in the EFThedron.