activity
20102026
most citedOn the classification of topological orders

177 citations · 633 across the 31 of their papers we have counts for

collaborators

34 papers

math.CT2026

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…

math-ph2023

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…

math.QA2021★ 46 cited

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…

hep-th2021★ 14 cited

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…

math.QA2020★ 15 cited

(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)-…

math.QA2020★ 24 cited

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…

math.AT2020

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…

math.CT2020★ 177 cited

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…

math.QA2019★ 11 cited

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…

math.CT2019★ 16 cited

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…

hep-th2019★ 1 cited

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…

hep-th2019★ 6 cited

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…

math.QA2018

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…

hep-th2018★ 42 cited

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,…

math.GR2018★ 6 cited

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.

hep-th2017★ 112 cited

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…

math.QA2017★ 23 cited

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…

math.GR2017★ 9 cited

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…

math.QA2016★ 1 cited

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…

math.SG2016★ 1 cited

The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

Theo Johnson-Freyd

We show that the Morita equivalences , , and arise from qu…

math.KT2015

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…

math-ph2015

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…

math-ph2015★ 12 cited

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…

math.CT2015★ 63 cited

(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…