Related papers: Holographic Subregion Complexity for Singular Surf…
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…
Arguments based on general principles of quantum mechanics have suggested that a minimum length associated with Planck-scale unification may in the context of the holographic principle entail a new kind of observable uncertainty in the…
We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate SO(5) global symmetry to its SO(4) subgroup. The weakly-coupled, six-dimensional gravity dual has regular geometry. One of…
Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this…
We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is…
Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the…
Holographic quantum error-correcting codes, often realized through tensor network architectures, have emerged as compelling toy models for exploring bulk-boundary duality in AdS-CFT. By encoding bulk information into highly entangled…
Computation of homology or cohomology is intrinsically a problem of high combinatorial complexity. Recently we proposed a new efficient algorithm for computing cohomologies of Lie algebras and superalgebras. This algorithm is based on…
We consider the holographic complexity conjectures in the context of the AdS soliton, which is the holographic dual of the ground state of a field theory on a torus with antiperiodic boundary conditions for fermions on one cycle. The…
This paper designs an alogrithm to compute the minimal combinations of finite sets in Euclidean spaces, and applys the algorithm of study the moment maps and geometric invariant stability of hypersurfaces. The classical example of cubic…
The holographic complexity of a 3+1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic complexity between the excited state and the ground state is then obtained. This is then related to the…
Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic…
The Laplace equation in the two-dimensional Euclidean plane is considered in the context of the inverse stereographic projection. The Lie algebra of the conformal group as the symmetry group of the Laplace equation can be represented solely…
We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of…
We enumerate complex algebraic hypersurfaces in $P^n$, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equi-singular strata in the…
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples,…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local…