Related papers: Algebraic Curves for Factorized String Solutions
There have been recent advances in the construction of algebraic curves for certain classes of string solutions in the context of the AdS/CFT correspondence. In this paper we obtain the Lax operators and associated spectral curves for…
Spectral curve methods proved to be powerful techniques in the context of relativistic integrable string theories, since they allow to derive the semiclassical spectrum from the minimal knowledge of a Lax pair and a classical string…
We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all…
In view of one day proving the AdS/CFT correspondence, a deeper understanding of string theory on certain curved backgrounds such as AdS_5xS^5 is required. In this dissertation we make a step in this direction by focusing on RxS^3. It was…
Factorization of string amplitudes is one way of constructing string interaction vertices. We show that correlation functions in string theory can be conveniently factorized using loop variables representing delta functionals. We illustrate…
For the homogeneous configuration given by the long string limit of the folded string with a spin in AdS3 and a spin and a winding number in S1, we solve the auxiliary linear problem in the finite-gap method and construct the Lax operator…
The algebraic curve (finite-gap) classification of rotating string solutions was very important in the development of integrability through comparison with analogous structures at weak coupling. The classification was based on the analysis…
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical…
We obtain many objects of discrete differential geometry as reductions of skew parallelogram nets, a system of lattice equations that may be formulated for any unit associative algebra. The Lax representation is linear in the spectral…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
Segmented strings in flat space are piecewise linear classical string solutions. Kinks between the segments move with the speed of light and their worldlines form a lattice on the worldsheet. This idea can be generalized to AdS$_3$ where…
We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…
We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…
Hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators. Here we show that hermitian symplectic spaces may also be used to describe the solution to the factorisation problem for the scattering…
A formula for factorizations of the full twist in the braid group $Br_{2m}$ depending on any four factorizations of the full twist in $Br_{m}$ is given. Applying this formula, a symplectic 4-manifold $X$ and two isotopic generic coverings…
We consider correlation functions for string theory on AdS_3. We analyze their singularities and we provide a physical interpretation for them. We explain which worldsheet correlation functions have a sensible physical interpretation in…
Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem,…