A note on connected formula for form factors

In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in ${\cal N}=4$ super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with $n$ massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators ${\rm Tr}(\phi^m)$ for arbitrary $m$.Comment: 13 page

On the Precise Laplace Approximation for Large Deviations of Markov Chain The Nondegenerate Case

Abstract. Let Ln be the empirical measure of a uniformly er-godic nonreversible Markov chain on a compact metric space and Φ be a smooth functional. This paper gives a precise asymptotic evalua-tion of the form E(exp(nΦ(Ln))) up to order 1 + o(1), in the case the Hessian of J −Φ is nondegenerate, where J is the rate function of the large deviations of empirical measure

Bridges Structural Health Monitoring and Deterioration Detection Synthesis of Knowledge and Technology

INE/AUTC 10.0

Globular Clusters in the Outer Halo of M31

In this paper, we present photometry of 53 globular clusters (GCs) in the M31 outer halo, including the {\sl GALEX} FUV and NUV, SDSS $ugriz$, 15 intermediate-band filters of BATC, and 2MASS $JHK_{\rm s}$ bands. By comparing the multicolour photometry with stellar population synthesis models, we determine the metallicities, ages, and masses for these GCs, aiming to probe the merging/accretion history of M31. We find no clear trend of metallicity and mass with the de-projected radius. The halo GCs with age younger than $\approx$ 8 Gyr are mostly located at the de-projected radii around 100 kpc, but this may be due to a selection effect. We also find that the halo GCs have consistent metallicities with their spatially-associated substructures, which provides further evidence of the physical association between them. Both the disk and halo GCs in M31 show a bimodal luminosity distribution. However, we should emphasize that there are more faint halo GCs which are not being seen in the disk. The bimodal luminosity function of the halo GCs may reflect different origin or evolution environment in their original hosts. The M31 halo GCs includes one intermediate metallicity group ($-1.5 <$ [Fe/H] $< -0.4$) and one metal-poor group ([Fe/H] $<-1.5$), while the disk GCs have one metal-rich group more. There are considerable differences between the halo GCs in M31 and the Milky Way (MW). The total number of M31 GCs is approximately three times more numerous than that of the MW, however, M31 has about six times the number of halo GCs in the MW. Compared to M31 halo GCs, the Galactic halo ones are mostly metal-poor. Both the numerous halo GCs and the higher-metallicity component are suggestive of an active merger history of M31.Comment: 14 pages, 16 figures, 6 tables. Accepted for publication in A&