177 citations · 633 across the 31 of their papers we have counts for
34 papers
On the structure of Witt groups and minimal extension conjecture
Theo Johnson-Freyd, Victor Ostrik, Zhiqiang Yu
Let be a Tannakian fusion category. For a braided fusion category over we give sufficient and necessary conditions that char…
Ground-state degeneracy of twisted sectors of Conway Moonshine SCFT
Alissa Furet, Theo Johnson-Freyd
We calculate the ground state degeneracies of all twisted sectors in the "Conway Moonshine'' holomorphic SCFT . We find that almost all sectors have ground states of…
Minimal nondegenerate extensions
Theo Johnson-Freyd, David Reutter
We prove that every slightly degenerate braided fusion category admits a minimal nondegenerate extension, and hence that every pseudo-unitary super modular tensor category admits a…
Topological Orders in (4+1)-Dimensions
Theo Johnson-Freyd, Matthew Yu
We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary cond…
(3+1)D topological orders with only a -charged particle
Theo Johnson-Freyd
There is exactly one bosonic (3+1)-dimensional topological order whose only nontrivial particle is an emergent boson: pure gauge theory. There are exactly two (3+1)-…
Fusion 2-categories with no line operators are grouplike
Theo Johnson-Freyd, Matthew Yu
We show that if is a fusion -category in which the endomorphism category of the unit object is or , then the indecomposable objects of $\math…
Topological Mathieu Moonshine
Theo Johnson-Freyd
We explore the Atiyah-Hirzebruch spectral sequence for the -cohomology of the classifying space of the largest Mathieu group , twisted by a…
On the classification of topological orders
Theo Johnson-Freyd
We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete -ca…
Supersymmetry and the Suzuki chain
Theo Johnson-Freyd
We classify SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which is not of type . The latter restriction makes the class…
Condensations in higher categories
Davide Gaiotto, Theo Johnson-Freyd
We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher…
Mock modularity and a secondary elliptic genus
Davide Gaiotto, Theo Johnson-Freyd
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard e…
A Note On Some Minimally Supersymmetric Models In Two Dimensions
D. Gaiotto, T. Johnson-Freyd, E. Witten
We explore the dynamics of a simple class of two-dimensional models with supersymmetry, namely sigma-models with target and the minimal possible set of fields. For an…
Galois action on VOA gauge anomalies
Theo Johnson-Freyd
Assuming regularity of the fixed subalgebra, any action of a finite group on a holomorphic VOA determines a gauge anomaly , where $\bold…
Holomorphic SCFTs with small index
Davide Gaiotto, Theo Johnson-Freyd
We observe that every self-dual ternary code determines a holomorphic N=1 superconformal field theory. This provides ternary constructions of some well-known holomorphic N=1 SCFTs,…
Third Homology of some Sporadic Finite Groups
Theo Johnson-Freyd, David Treumann
We compute the integral third homology of most of the sporadic finite simple groups and of their central extensions.
Symmetry Protected Topological phases and Generalized Cohomology
Davide Gaiotto, Theo Johnson-Freyd
We discuss the classification of SPT phases in condensed matter systems. We review Kitaev's argument that SPT phases are classified by a generalized cohomology theory, valued in th…
The Moonshine Anomaly
Theo Johnson-Freyd
The anomaly for the Monster group acting on its natural (aka moonshine) representation is a particular cohomology class $ω^\natural \in \mathrm{H}^3(\math…
Theo Johnson-Freyd, David Treumann
We show that the fourth integral cohomology of Conway's group is a cyclic group of order , generated by the first fractional Pontryagin class of the -dimens…
Exact triangles, Koszul duality, and coisotopic boundary conditions
Theo Johnson-Freyd
We develop a theory of "arrowed" (operads and) dioperads, which are to exact triangles as dioperads are to vector spaces. A central example to this paper is the arrowed operad cont…
The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
Theo Johnson-Freyd
We show that the Morita equivalences , , and arise from qu…
Exact triangles as modules over an -category
Theo Johnson-Freyd
This note describes a strictly-unital -category whose representations are exact triangles such that the three-fold symmetry on exact triangles is manifest on the $A_\inft…
Heisenberg-picture quantum field theory
Theo Johnson-Freyd
What we should mean by "Heisenberg-picture quantum field theory"? Atiyah--Segal-type axioms do a good job of capturing the "Schrödinger picture": these axioms define a "-dimensi…
Spin, statistics, orientations, unitarity
Theo Johnson-Freyd
A topological quantum field theory is Hermitian if it is both oriented and complex-valued, and orientation-reversal agrees with complex-conjugation. A field theory satisfies spin-s…
(Op)lax natural transformations, twisted quantum field theories, and "even higher" Morita categories
Theo Johnson-Freyd, Claudia Scheimbauer
Motivated by the challenge of defining twisted quantum field theories in the context of higher categories, we develop a general framework for lax and oplax transformations and thei…