Related papers: Asyzygies, modular forms, and the superstring meas…
Quasicircular binary black hole mergers are described by 15 parameters, of which gravitational wave observations can typically constrain only $\sim 10$ independent combinations to varying degree. In this work, we devise coordinates that…
Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and…
A discussion of asymptotic weak and strong Poincare' charges in metric gravity is given to identify the proper Hamiltonian boundary conditions. The asymptotic part of the lapse and shift functions is put equal to their analogues on…
We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lov\'asz theta number to Cayley graphs on the special orthogonal group…
Precise formulas are derived for the expected values $<\xi>$, $<\eta>$ and variances $\delta \xi ^2$, $\delta \eta ^2$ of random variables $\xi$, $\eta$ describing the spin asymmetry of some reaction when a background process contribution…
The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX,…
Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization…
For superstrings, the consequences of replacing the measure of integration $\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric $\gamma_{ab}$…
We constrain the spectrum of $\mathcal{N}=(1, 1)$ and $\mathcal{N}=(2, 2)$ superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the $\Gamma_\theta$ congruence subgroup of the…
Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge…
We consider random systems of equations x_1 + ... + x_k = a; 0 <= a <= 2 which are interpreted as equations modulo 3: We show for k >= 15 that the satisfiability threshold of such systems occurs where the 2-core has density 1: We show a…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
We present the {\it canonical} set of superspace constraints for self-dual supergravity, a ``self-dual'' tensor multiplet and a self-dual Yang-Mills multiplet with $~N=1~$ supersymmetry in the space-time with signature $(+,+,-,-)$. For this…
The problem of boundary conditions in a supersymmetric theory of quantum cosmology is studied, with application to the one-loop prefactor in the quantum amplitude. Our background cosmological model is flat Euclidean space bounded by a…
Three-loop counterterms for the Standard Model (SM) revealed that the matrix of anomalous dimensions ($\gamma$) of quarks is divergent in the $d \to 4$ limit unless a carefully chosen non-Hermitian square-root of $Z$ matrix is used in the…
We employ the derivative expansion of the nonperturbative renormalization group to address the phenomenon of anisotropic scale invariance and the associated functional fixed points, also known as Lifshitz points, in systems characterized by…
Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry.…
The quantum mechanical definition of probability, the uncertainty principle and Poincare invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of…
We explicitly analyse $O(\alpha')$ corrections to heterotic supergravity on toroidal orbifolds and their resolutions, which play important roles in string phenomenology as well as moduli stabilisation. Using a conformal factor ansatz that…