Related papers: Cobordism and Deformation Class of the Standard Mo…
Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on a systematic cobordism classification, we examine constraints from invertible quantum…
We classify and characterize all invertible anomalies and all allowed topological terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we mean the inclusion…
We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric pure…
The local Lie algebra of the Standard Model (SM) is $su(3)\times su(2) \times u(1)$, yet its global gauge group, $G_{{\rm SM}_{\rm q}}=$SU(3)$\times$SU(2)$\times$U(1)/$\mathbb{Z}_{\rm q}$, q$=1,2,3,6$ remains undetermined. Building on…
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…
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…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
We formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging $G$-equivariant invertible spin-TQFTs, or, in physics language,…
We study generalized global symmetries and their 't Hooft anomalies in 3d N=4 superconformal field theories (SCFTs). Following some general considerations, we focus on good quiver gauge theories, comprised of balanced unitary nodes and…
We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a…
In this paper, we construct new models for the Anderson duals $(I\Omega^G)^*$ to the stable tangential $G$-bordism theories and their differential extensions. The cohomology theory $(I\Omega^G)^*$ is conjectured by Freed and Hopkins [FH21]…
A recent work [2006.16996] suggests that a 4d nonperturbative global anomaly of mod 16 class hinting a possible new hidden gapped topological sector beyond the Standard Model (SM) and Georgi-Glashow $su(5)$ Grand Unified Theory (GUT) with…
Consider a d-dimensional quantum field theory (QFT) $\mathfrak{T}$, with a generalized symmetry $\mathcal{S}$, which may or may not be invertible. We study the action of $\mathcal{S}$ on generalized or $q$-charges, i.e. $q$-dimensional…
We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on $\mathbb{Z}_N$ one-form symmetries. A 3d topological quantum field theory (TQFT) $\mathcal{T}$…
We systematically study Lorentz symmetry extensions in quantum field theories (QFTs) and their 't Hooft anomalies via cobordism. The total symmetry $G'$ can be expressed in terms of the extension of Lorentz symmetry $G_L$ by an internal…
Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4-dimensional fermionic anomalies with discrete $Z_n$ symmetry, classified by the 5d spin…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These {\lambda}-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G…
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
We investigate the interplay between (-1)-form symmetries and their quantum-dual (d-1)-form counterparts within the framework of Symmetry Topological Field Theories (SymTFTs). In this framework the phenomenon of decomposition -- a…