Submissions from K. Nakajima
-  faKiv:1911.07231 [pdf]
A note on effective field theories in 3+1 dimensionsComments: 5 pages, 1 figure
The efficiency of the effective field theory (EFT) is spatially dependent on the number of dimensions and the spatial dimension of the spaces involved. While other topological methods are available for any number of dimensions, the EFT can only be formulated in terms of the maximal area of the space in which the scattering amplitude and the energy are both maximal. In this paper, we study the quadratic effective EFT in three dimensions, which has the same number of dimensions as the three-dimensional EFT but is given by the Squarespace Index of a four-dimensional superconformal field theory. We show that the quadratic EFT is the effective EFT for fermions in three dimensions, which is the same as the topologically-invariant quadratic EFT for fermions in three dimensions. We then show that the quadratic EFT can be implemented in terms of the Squarespace Index of a five-dimensional superconformal field theory, which is the same as the quadratic EFT of a five-dimensional superconformal field theory.