Related papers: Global Structures from the Infrared

Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…

Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their…

The local Lie algebra of the Standard Model (SM) is $su(3)\times su(2) \times u(1)$, yet its global gauge group, $G_{{\rm SM}_{\rm q}}=$SU(3)$\times$SU(2)$\times$U(1)/$\mathbb{Z}_{\rm q}$, q$=1,2,3,6$ remains undetermined. Building on…

We investigate options for the structure of the infrared fixed points of $\mathcal{N}=4$ bad theories in three dimensions. Unitarity constraints allow a number of possibilities, not necessarily a product of an interacting $\mathcal{N}=4$…

We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary…

We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…

This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…

We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized…

Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically…

We introduce an effective field theory (EFT) for conformal impurity by considering a pair of transversely displaced impurities and integrating out modes with mass inversely proportional to the separation distance. This EFT captures the…

A recently conjectured relashionship between UV and IR cutoffs in an effective field theory without quantum gravity is generalized in the presence of large extra dimensions. Estimates for the corrections to the usual calculation of…

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary,…

We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…

We provide an informal discussion of pattern formation in a finite universe. The global size and shape of the universe is revealed in the pattern of hot and cold spots in the cosmic microwave background. Topological pattern formation can be…

Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted…

This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…

I briefly summarize a recent research program aiming to probe the landscape of low-energy phases of string theory from a global perspective. Borrowing conceptual lessons from the swampland program, I will discuss how the effective theories…

Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic…

Varying the curvature, quantum phase transitions are investigated in holographic confining QFTs defined on a fixed constant positive curvature background. We find a competition between two branches of solutions and a phase transition as one…

We propose a general framework to characterize gapped infra-red (IR) phases of theories with non-invertible (or categorical) symmetries. In this paper we focus on (1+1)d gapped phases with fusion category symmetries. The approach that we…