Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in N=2 minimal models. The results are expressed in terms of integrals of conformal blocks and evaluated numerically in the alpha' expansion. We find striking agreements with up to 2-loop scattering amplitudes of massless gluons in 6D SU(k) SYM at a Z_k invariant point on the Coulomb branch. We comment on the issue of UV divergence at higher loop orders in the gauge theory and discuss the implication of our results.Comment: 58 pages, 5 figures, 3 tables, comments added, references adde

Topological Defect Lines and Renormalization Group Flows in Two Dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.Comment: 101 pages, 63 figures, 2 tables; v3: minor changes, added footnotes and references, published versio

Geometric Element Test Targets for Visual Inference of a Printer\u27s Dimension Limitations

As technologies advance in the field of additive manufacturing (AM), it increases the demand in using test targets to quantitatively appraise the performance of AM processes and parts. This study presents a unique concept to address the dimensional and geometric viability of three-dimensional (3D) printers with test targets that are unique and complementary to those currently available. We have named these distinct designed artifacts as Geometric Element Test Targets (GETTs(TM)). The concept for the targets is to rely on positioning and spatial frequency of geometric shapes to induce failures that are indicative of the system’s dimensional limitations. A distinguishing characteristic is that the dimensional failures can be inspected visually. Systematic evaluations of the limitations can be further conducted through contact or non-contact measurements. The initial GETTs(TM) include three suites of test targets: line, angular and circular suites. We will illustrate this concept with samples produced with fused deposition modeling printers. The potential applications of GETTs(TM) include standardization, reference targets, in-line system control, and more

3d N=4 Bootstrap and Mirror Symmetry

We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$ theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with $SU(2) \times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry thereof

Topological Defect Lines and Renormalization Group Flows in Two Dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the ’t Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance

Protective Effects of Total Saponins of Panax Notoginseng on Steroid-Induced Avascular Necrosis of the Femoral Head In Vivo and In Vitro

This research was designed to investigate the protective effects of TSPN on steroid-induced avascular necrosis of the femoral head (ANFH) and the likely mechanisms of those effects. As an in vivo study, TSPN was shown to be protective against steroid-induced ANFH due to the upregulation of VEGF-A. Furthermore, TSPN attenuated the apoptosis of osteocytes and reduced the expression of Caspase-3 relative to the model group. As an in vitro study, TSPN exerted a concentration-dependent protective effect against apoptosis in MC3T3-E1 cells. Moreover, TSPN (at a dose of 100 μg/mL) significantly reversed the dexamethasone-induced augmentation of Caspase-3 expression and activity. Therefore, our study demonstrated that TSPN had a protective effect against steroid-induced ANFH that was related to the upregulation of VEGF-A and the inhibition of apoptosis and Caspase-3 activation