Determining an infinite-dimensional Fermionic de Sitter space for noncommutative QFTs

Pierluigi Muzzi, Rafael Kyriaki, James Shkolnik
Comments: 31 pages plus appendices

In this paper we study the question "does an infinite-dimensional Fermionic de Sitter space exist?" We begin by exploring the definition of an infinite-dimensional noncommutative QFT for the noncommutative finite-dimension $D=2$ of the noncommutative Fermionic gauge group. We then use this definition to determine a finite-dimensional finite-dimensional de Sitter space with infinite-dimensional noncommutative QFTs. We show that such a de Sitter space admits a null-energy condition. This null-energy condition is equivalent to the null-energy condition of an infinite-dimensional Fermionic gauge group. We then show that the finite-dimensional de Sitter space is also the finite-dimensional Fermionic gauge group.