13 research outputs found
Reflection positivity and invertible topological phases
We implement an extended version of reflection positivity (Wick-rotated
unitarity) for invertible topological quantum field theories and compute the
abelian group of deformation classes using stable homotopy theory. We apply
these field theory considerations to lattice systems, assuming the existence
and validity of low energy effective field theory approximations, and thereby
produce a general formula for the group of Symmetry Protected Topological (SPT)
phases in terms of Thom's bordism spectra; the only input is the dimension and
symmetry group. We provide computations for fermionic systems in physically
relevant dimensions. Other topics include symmetry in quantum field theories, a
relativistic 10-fold way, the homotopy theory of relativistic free fermions,
and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3
major revision; v4 minor revision: corrected proof of Lemma 9.55, many small
changes throughout; v5 version for publication in Geometry & Topolog
Q(sqrt(-3))-Integral Points on a Mordell Curve
We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4