Related papers: Complexity measures from geometric actions on Vira…
The subject of our study is the Kazhdan-Lusztig (KL) equivalence in the context of a one-parameter family of logarithmic CFTs based on Virasoro symmetry with the (1,p) central charge. All finite-dimensional indecomposable modules of the…
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…
Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…
We perform the Hamiltonian reduction of Lower Spin Gravity, the simplest bulk dual for a Warped Conformal Field Theory (WCFT), consisting in an $SL(2) \times U(1)$ Chern-Simons model. We identify the boundary action as the geometric action…
We rewrite the Chern-Simons description of pure gravity on global AdS$_3$ and on Euclidean BTZ black holes as a quantum field theory on the AdS boundary. The resulting theory is (two copies of) the path integral quantization of a certain…
In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of…
A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints…
We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS$_3$/CFT$_2$ correspondence. To give such an interpretation in previous studies, certain restrictions…
We study the "complexity equals volume" (CV) and "complexity equals action" (CA) conjectures by examining moments of of time symmetry for $\rm AdS_3$ wormholes having $n$ asymptotic regions and arbitrary (orientable) internal topology. For…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
We study the visual complexity of animated transitions between point sets. Although there exist many metrics for point set similarity, these metrics are not adequate for this purpose, as they typically treat each point separately. Instead,…
We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
We discuss the quantization and holographic aspects of a class of conical spaces in 2+1 dimensional pure AdS gravity. These appear as topological solitons in the Chern-Simons formulation of the theory and are closely related to the recently…
We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
We study rigidity and stability of infinite dimensional algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes,…
Kinematics of mechanisms is intricately coupled to their geometry and their utility often arises out of the ability to perform reproducible motion with fewer actuating degrees of freedom. In this article, we explore the assembly of…