Related papers: Field theories with higher-group symmetry from com…
Six-dimensional superconformal field theories (6D SCFTs) occupy a central place in the study of quantum field theories encountered in high energy theory. This article reviews the top down construction and study of this rich class of quantum…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We determine the $d+1$ dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for $d$-dimensional QFTs obtained by compactifying M-theory on a non-compact space $X$. The resulting theory,…
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a…
Grand unified theory defined on higher-dimensional orbifolds provides a new way to solve the hierarchy problem. In gauge theory on an orbifold many different sets of boundary conditions imposed at orbifold fixed points (branes) are related…
We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is non-supersymmetric at high scales,…
Higher-form symmetries act on sub-dimensional spatial manifolds of a quantum system. They can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level, making them difficult to characterize.…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d…
We study the low-energy dynamics of systems with exact and approximate higher-form symmetries using gauge/gravity duality. These symmetries are realised holographically via Maxwell-type theories for massless and massive $p$-forms in AlAdS…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some non vanishing values at spatial infinity. In this case the Gauss constraint only eliminates…
Various nonsupersymmetric theories at large but finite $N$ are argued to permit light scalars and large hierarchies without fine-tuning. In a dual string description, the hierarchy results from competition between classical and quantum…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…
The invention of supersymmetry, almost exactly 25 years ago, changed the face of high-energy physics. The idea that the observed low-energy gauge groups appear due to the process of spontaneous breaking of a single unifying group $G$ is…
We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry…
In this paper it is proved that near a compact, invariant, proper subset of a continuous flow on a compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. This result shows…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
We argue that higher spin fields originate from Hamiltonian mechanics and play a role of gauge fields ensuring covariance of geometric observables such as length and volume with respect to canonical transformations in the same way as a…