Harvard

Electric 1-form symmetries are generically broken in gauge theories with Chern-Simons terms. In this talk we discuss how infinite subsets of these symmetries become non-invertible topological defects. Time permitting we will also discuss generalizations and applications to the Swampland program in relation to the completeness hypothesis.

There have been several proposals of scale-separated AdS vacua in the literature. All known examples arise from the effective field theory of flux compactifications with low supersymmetry, and there are often doubts about their consistency as 10 or 11d backgrounds in string theory. These issues can often be tackled in the bulk theory, or by analysis of the dual CFT via holography. I will review the most common issues, and focus the analysis on the recently constructed family of 3d scale-separated AdS vacua, which is dual to a two-dimensional CFT, emphasizing the discrete symmetry structure of the model in comparison to DGKT. Finally, I will comment on the tantalizing observation of integer operator dimensions in DGKT-like vacua, and comment on possible places to look for consistency issues in these models.

We discuss the formal relationship between the absence of global symmetries and completeness, both in effective field theory and in quantum gravity. In effective field theory, we must broaden our notion of symmetry to include non-invertible topological operators. However, in gravity, the story is simplified as the result of charged gravitational solitons.

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. I will also discuss how this correspondence is modified in more general contexts, including e.g. Chern-Simons terms. 

Biological systems provide an inspiration for creating a new paradigm
for materials synthesis. What would it take to enable inanimate material
to acquire the properties of living things? A key difference between
living and synthetic materials is that the former are programmed to
behave as they do, through interactions, energy consumption and so
forth. The nature of the program is the result of billions of years of
evolution. Understanding and emulating this program in materials that
are synthesizable in the lab is a grand challenge. At its core is an
optimization problem: how do we choose the properties of material
components that we can create in the lab to carry out complex reactions?
I will discuss our (not-yet-terribly-successful efforts)  to date to
address this problem, by designing both equiliibrium and kinetic 
properties of materials, using a combination of statistical mechanics,
kinetic modeling and ideas from machine learning.

I will lead an informal discussion centered on discrete data that need to be specified when reducing 6d relative theories on an internal manifold M and how they determine symmetries of the resulting theory T[M].

We explore general constraints from unitarity, defect superconformal symmetry and locality of bulk-defect couplings to classify possible superconformal defects in superconformal field theories (SCFT) of spacetime dimensions d>2.  Despite the general absence of locally conserved currents, the defect CFT contains new distinguished operators with protected quantum numbers that account for the broken bulk symmetries.  Consistency with the preserved superconformal symmetry and unitarity requires that such operators arrange into unitarity multiplets of the defect superconformal algebra, which in turn leads to nontrivial constraints on what kinds of defects are admissible in a given SCFT.  We will focus on the case of superconformal lines in this talk and comment on several interesting implications of our analysis, such as symmetry-enforced defect conformal manifolds, defect RG flows and possible nontrivial one-form symmetries in various SCFTs.  

Kirigami, the relatively unheralded cousin of origami, is the art of cutting paper to articulate and deploy it as a whole. By varying the number, size, orientation and coordination of the cuts, artists have used their imagination and intuition to create remarkable sculptures in 2 and 3 dimensions. I will describe some of our attempts to quantify the inverse problem that artists routinely solve, combining elementary mathematical ideas, with computations and physical models. 

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