Related papers: Spin-cobordisms, surgeries and fermionic modular b…
The Arf-Brown invariant $\mathit{AB}(\Sigma)$ is an 8th root of unity associated to a surface $\Sigma$ equipped with a pin$^-$ structure. In this note we investigate a certain fully extended, invertible, topological quantum field theory…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by…
In this note, we propose an extension of the relation between worldsheet global symmetries and structures over moduli spaces of superconformal field theories (SCFTs) to include noninvertible symmetries. The most familiar examples of such…
We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying…
A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that…
't Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a $d$d spacetime are known to be classified by a $d+1$d cobordism group TP$_{d+1}$(G), whose group…
Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…
The moduli space and generalised global symmetries of 3d $\mathcal{N} = 5$ superconformal field theories are investigated, with a focus on the orthosymplectic ABJ theories and their discrete gauging variants. We extend the known…
We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines…
We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension…
Any local unitary 3d $\mathcal{N}=4$ superconformal field theory (SCFT) has a corresponding "universal" relevant deformation that takes it to a gapped phase. This deformation preserves all continuous internal symmetries, $\mathcal{S}$, and…
Quantum field theory has various projective characteristics which are captured by what are called anomalies. This paper explores this idea in the context of fully-extended three-dimensional topological quantum field theories (TQFTs). Given…
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…
It is well-known that conformal embeddings can be used to construct non-diagonal modular invariants for affine lie algebras. This idea can be extended to construct infinite series of non-diagonal modular invariants for coset CFTs. In this…
This is a study of algebras with involution that become isomorphic over a separable closure of the base field to a tensor product of two composition algebras. We classify these algebras, provide criteria for isomorphism and isotopy, and…
The Tambara-Yamagami (TY) fusion category symmetry $\text{TY}(\mathbb{A},\chi,\epsilon)$ describes the enhanced non-invertible self-duality symmetry of a $2$-dim QFT under gauging a finite Abelian group $\mathbb{A}$. We generalize the…
For a positive integer r, an r-spin topological quantum field theory is a 2-dimensional TQFT with tangential structure given by the r-fold cover of SO_2 . In particular, such a TQFT assigns a scalar invariant to every closed r-spin surface…
Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter $t$, that have…
We show that certain 't~Hooft anomalies that evade detection on commonly used closed four-dimensional manifolds become visible when a quantum field theory is placed on asymptotically locally Euclidean (ALE) spaces. As a concrete example, we…