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