Related papers: Modified Partition Functions, Consistent Anomalies…
We determine all the terms that are gauge-invariant up to a total spacetime derivative ("semi-invariant terms") for gauged non-linear sigma models. Assuming that the isotropy subgroup $H$ of the gauge group is compact or semi-simple, we…
In this talk, we briefly review the basic concepts of anomalous gauge theories. It has been known for some time how theories with local anomalies can be handled. Recently it has been pointed out that global anomalies, which obstruct the…
Partition functions of some two-dimensional statistical models can be represented by means of Grassmann integrals over loops living on two-dimensional torus. It is shown that those Grassmann integrals are topological invariants, which…
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show…
The gauging of axionic, Stueckelberg-type, shift symmetries with generalized Chern-Simons terms and the Green-Schwarz mechanism of anomaly cancellation has recently been studied in the context of certain string compactifications and with…
Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or…
There are different operators of quark and gluon momenta, orbital angular momenta, and gluon spin in the nucleon structure study. The precise meaning of these operators are studied based on gauge invariance, Lorentz covariance and canonical…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
In particle physics, the fundamental forces are subject to symmetries called gauge invariance. It is a redundancy in the mathematical description of any physical system. In this article I will demonstrate that the transformer architecture…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
A gauge-independent approach to resonant transition amplitudes with nonconserved external currents is presented, which is implemented by the pinch technique. The analytic expressions derived with this method are $U(1)_{em}$ invariant,…
We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…
Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $\tau_k(n)$, is defined as follows:…
We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…