Categorical Symmetry of the Standard Model from Gravitational Anomaly

A global symmetry of a quantum field theory is said to have an 't Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in ...

The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By classification of quantum anomalies and symmetric invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and the existence of symmetric gapped boundary for the trivial symmetric invertible topological orders, we propose that Spi...

The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation: space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F. The raison d'etre for F is to correct the K-theoretic dimension from four to ten (modulo eight). We classify th...

Recently it has been observed that branes in geometric engineering and holography have a striking connection with generalized global symmetries. In this paper we argue that branes, in a certain topological limit, not only furnish the symmetry generators, but also encode the so-called Symmetry Topological Field Theory (or SymTFT). For a $d$-dimensional QFT, this is a $(d+1)$-dimensional topological field theory, whose topological defects encode both the symmetry generators (in...

We argue that a cosmic neutrino background that carries non-zero lepton charge develops gravitational instabilities. Fundamentally, these instabilities are related to the mixed gravity-lepton number anomaly. We have explicitly computed the gravitational Chern-Simons term which is generated quantum-mechanically in the effective action in the presence of a lepton number asymmetric neutrino background. The induced Chern-Simons term has a twofold effect: (i) gravitational waves p...

I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern SU(5) to SU(3)xSU(2)xU(1) is preferred over the pattern SU(5) to SU(4)xU(1). On the basis of the argument one expects an asymmetry in the early universe microwave data, which might have been detected already.

We argue that quantum electrodynamics combined with quantum gravity results in a new source of CP violation, anomalous non-conservation of chiral charge and quantisation of electric charge. Further phenomenological and cosmological implications of this observation are briefly discussed within the standard model of particle physics and cosmology

The standard electroweak model with Dirac neutrinos is extended by way of the principles of electroweak quark-lepton symmetry and weak topological-charge confinement to account for quark-lepton charge relations which, if not accidental, are indicative of charge structures. A mixing in quarks and leptons of underlying integer local charges with integer weak topological charges associated with an additive group Z_3, fixed by the anomaly cancellation requirement, is discussed. I...

In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group G (which can be continuous or discrete). We show a very close relation between gauge anomalies and symmetry-protected trivial (SPT) orders [also known as symmetry-protected topological (SPT) orders] in one-higher dimensions. Using such an idea, we argue that, in d space-time dimensions, the gauge anomalies are described by the elements in Free[H^{d+1}(...

In a minimal extension of the Standard Model, in which new neutral fermions have been introduced, we show that the requirement of vanishing anomalies fixes the hypercharges of all fermions uniquely. This naturally leads to electric charge quantization in this minimal scenario which has features similar to the Standard Model: invariance under the gauge group $SU(2)_L\otimes U(1)_Y$, conservation of the total lepton number and masslessness for the ordinary neutrinos. Such minim...