Near-flat Space Research Articles

Proposing spacetime scale for space tourism economics

This research proposes the spacetime scale to derive a space tourism economic model based on the General Relativity Theory. The space curvature is considered in the economic model analogized to a physic theory to expand the horizons of tourism economics. The deductive reasoning and analogy methods were adopted to propose the spacetime scale for space tourism economics, accommodating the conventional economic models of near-flat space commodities on the earth. Conclusions suggest conquering our perception acceptance from linear time to curvilinear spacetime for space tourism economics.

The Reconstruction of Dark Energy with the Ridge Regression Approach

Abstract Whether or not dark energy evolves with time may be determined by the nonparametric method. In order to avoid instability of the derivative for the functional data, we linearize the luminosity-distance integral formula in near-flat space by adopting Lagrange interpolation for the numerical integral, and proposing a method of combining principal component analysis (PCA) and biased estimation on the basis of ridge regression analysis to reconstruct the regression parameters. We also present a principal component selection criterion to better distinguish between ΛCDM and w(z) ≠ −1 models by reconstruction. We define the type I error as the situation where w true = −1 but w recon ≠ −1, and the type II error as the situation where w true ≠ −1 but w recon = −1; we use the various w(z) functions to test the method. The preliminary test results demonstrate that the PCA-biased method can be used to determine the most probable behavior of w(z). Finally, we apply this method to recent supernova measurements, reconstructing the continuous history of w(z) out to redshift z = 1.5.

Worldsheet scattering in AdS3/CFT2

We confront the recently proposed exact S-matrices for AdS 3/CFT 2 with direct worldsheet calculations. Utilizing the BMN and Near Flat Space (NFS) expansions for strings on AdS 3 × S 3 × S 3 × S 1 and AdS 3 × S 3 × T 4 we compute both tree-level and one-loop scattering amplitudes. Up to some minor issues we find nice agreement in the tree-level sector. At the one-loop level however we find that certain non-zero tree-level processes, which are not visible in the exact solution, contribute, via the optical theorem, and give an apparent mismatch for certain amplitudes. Furthermore we find that a proposed one-loop modification of the dressing phase correctly reproduces the worldsheet calculation while the standard Hernandez-Lopez phase does not. We also compute several massless to massless processes.

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.

Near-flat space limit of strings on AdS 4×ℂℙ3

The non-linear nature of string theory on non-trivial backgrounds, related to the AdS/CFT correspondence, force one to look for simplifications. Two such simplifications proved to be useful in studying string theory. These are the pp-wave limit, which describes point-like strings, and the so-called “near-flat space” limit which connects two different sectors of string theory—pp-wave and “giant magnons”. Recently another example of AdS/CFT duality emerged—AdS 4/CFT 3, which suggests duality between \(\mathcal{N}=6\) CS theory and superstring theory on \(\mathit{AdS}_{4}\times \mathbb{CP}^{3}\) . In this paper we study the “near-flat space” limit of strings on an \(\mathit{AdS}_{4}\times \mathbb{CP}^{3}\) background and discuss possible applications of the limiting theory.

Algebra of transfer-matrices and Yang–Baxter equations on the string worldsheet in [formula omitted

Integrability of the string worldsheet theory in AdS 5 × S 5 is related to the existence of a flat connection depending on the spectral parameter. The transfer matrix is the open-ended Wilson line of this flat connection. We study the product of transfer matrices in the near-flat space expansion of the AdS 5 × S 5 string theory in the pure spinor formalism. The natural operations on Wilson lines with insertions are described in terms of r- and s-matrices satisfying a generalized classical Yang–Baxter equation. The formalism is especially transparent for infinite or closed Wilson lines with simple gauge invariant insertions.

Near-flat space limit and Einstein manifolds

We study the near-flat space limit for strings on AdS5 × M5, where the internal manifold M5 is equipped with a generic metric with U(1)3 isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS5 × S5, as the global symmetries are reduced in the most general case. When M5 is a Sasaki-Einstein space like T1,1, Yp,q and Lp,q,r, whose dual CFT's have = 1 supersymmetry, the near-flat space limit gives the same bosonic sector of the sigma model found for AdS5 × S5. This indicates the generic presence of integrable subsectors in AdS/CFT.