Related papers: Prescriptive Unitarity and Rigidity at Two Loops
We investigate the elliptic analogs of multi-indexed polylogarithms that appear in the theory of the fundamental group of the projective line minus three points as sections of a universal nilpotent bundle with regular singular connection.…
This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
We consider the problem of proving termination for triangular weakly non-linear loops (twn-loops) over some ring $\mathcal{S}$ like $\mathbb{Z}$, $\mathbb{Q}$, or $\mathbb{R}$. The guard of such a loop is an arbitrary quantifier-free…
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus…
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
We unify and generalize different notions of local units and local projectivity. We investigate the connection between these properties by constructing elementary algebras from locally projective modules. Dual versions of these…
We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as…
We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N = 8 supergravity at the fifth post-Minkowskian order to next-to-leading order in a…
The high-energy limit of $2\to 2$ scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex…
We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…
A wealth of literature exists on computing and visualizing cuts for the magnetic scalar potential of a current carrying conductor via Finite Element Methods (FEM) and harmonic maps to the circle. By a cut we refer to an orientable surface…
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the…
We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…
We elaborate on aspects of a new positive geometry proposed recently, which was conjectured to be the four-point amplituhedron for ABJM theory. We study generalized unitarity cuts from the geometry, and in particular we prove that (1) the…
We describe the recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD. The method combines the unitarity method with loop-level on-shell recursion. The unitarity method is used to…
Quantum LDPC codes have attracted intense interest due to their advantageous properties for realizing efficient fault-tolerant quantum computing. In particular, sheaf codes represent a novel framework that encompasses all well-known good…