This week

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Quantum theories of gravity are generally expected to have some degree of nonlocality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy slices provides an interesting laboratory in which this emergence can be explored. In this context, the remaining isometries are gauge symmetries and, as a result, gauge-invariant observables cannot be localized. Instead, local physics can arise only through certain relational constructions. In this talk, we explore such issues for perturbative quantum gravity around de Sitter space. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal hypersphere in dS, this approximation can be accurate only over regions in which the corresponding global time coordinate spans an interval of order ln G^(-1). In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dS so long as those regions are located far to the future or past of such a minimal sphere. This talk is based on the paper arXiv:2410.00111 with Donald Marolf, Xuyang Yu, and Ying Zhao.

A recently introduced class of 5d superconformal field theories (SCFTs), dubbed 5d conformal matter (CM) in reference to the well known 6d CM theories, is constructed in M-theory on Calabi-Yau threefolds (CY3s) which can be viewed as intersecting ADE singularities. I will address the classification of these theories - based on the weight lattice of ADE algebras - which fall into three classes: Atoms, Molecules, and so called Hybrids. I will show how these three types are distinguished by their geometric construction. Further we will explore the brane constructions dual to the CY3s where possible, the quantum Higgs branch of the 5d CM theories, and the circle reduction to 4 dimensions.