Related papers: Fermionic Modular Categories and the 16-fold Way
We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite $G$-symmetry. In particular, we argue that (3+1)d fermionic topological order with $G$-symmetry correspond to…
We study the phase diagram of one dimensional spin one-half fermionic cold atoms. The two ``spin'' species can have different hopping or mass. The phase diagram at equal densities of the species is found to be very rich, Mott insulators as…
This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal…
Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played…
Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $\sigma$. Under suitable conditions on $V$, the $\sigma$-fixed subspace $V_{\bar 0}$ is a vertex operator algebra and the category $C_{V_{\bar 0}}$ of $V_{\bar…
We consider general fermionic quantum field theories with a global finite group symmetry $G$, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with…
We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based…
The M$_k$ models for 1D lattice fermions are characterised by ${\cal N}=2$ supersymmetry and by an order-$k$ clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton…
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…
The problem of meson bound states with $N_f$ massive fermions in two dimensional quantum electrodynamics is discussed. We speculate about the spectrum of the lightest particles by means of the effective semiclassical description. In…
The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted equivariant K-theory. We build on their work to…
We construct deformation invariants of $2|1$-dimensional Euclidean field theories valued in a cohomology theory approximating topological modular forms. This implies several results anticipated by Stolz and Teichner and gives the first…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We extend the periodic table of phases of free fermions in the ten-fold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry $\hat G$ in an arbitrary dimension. The…
It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank $n$. This follows from a double-exponential bound on the maximal denominator in an Egyptian…
We develop covariant fermionic fields of space-like particles. As an application of the formalism we discuss the example of superluminous tachyons with imaginary rest mass and spin 1/2 forming fermionic ensembles that is relativistically…