arXiv subjects
Publications and source records attributed to Keith C. Hannabuss.
String-theoretic T-duality can be exploited to simplify some features of the bulk-boundary correspondence in condensed matter theory. This paper surveys how T-duality links position and momentum space pictures of that correspondence.
We state and prove a general result establishing that T-duality simplifies the bulk-boundary correspondence, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors, and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to String Theory and to the study of the quantum Hall effect and topological insulators with defects in Condensed Matter Physics.
We analyse the recursive formula found for various Ext groups for $\SL_2(k)$, $k$ a field of characteristic $p$, and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of $\SL_2(k)$ is at least exponential. In particular, $\max \{\dim \Ext^i_{\SL_2(k)}(k, Δ(a))\mid a,i \in \N \}$ has (at least) exponential growth for all $p$. We also show that $\max \{\dim \Ext^i_{\SL_2(k)}(k, Δ(a))\mid a\in \N \}$ for a fixed $i$ is bounded.
Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be regarded as a braided Clifford algebra over a braided commutative boson algebra, sharing much of the structure of ordinary Clifford algebras.