On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT

We consider the 2-point function of string vertex operators representing string state with large spin in AdS_5. We compute this correlator in the semiclassical approximation and show that it has the expected (on the basis of state-operator correspondence) form of the strong-coupling limit of the 2-point function of single trace minimal twist operators in gauge theory. The semiclassical solution representing the stationary point of the path integral with two vertex operator insertions is found to be related to the large spin limit of the folded spinning string solution by a euclidean continuation, transformation to Poincare coordinates and conformal map from cylinder to complex plane. The role of the source terms coming from the vertex operator insertions is to specify the parameters of the solution in terms of quantum numbers (dimension and spin) of the corresponding string state. Understanding further how similar semiclassical methods may work for 3-point functions may shed light on strong-coupling limit of the corresponding correlators in gauge theory as was recently suggested by Janik et al in arXiv:1002.4613.Comment: 19 pages, 1 figure; minor corrections, references added, footnote below eq. (4.5) adde

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Integrable Background Geometries

This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric structure, governed by a nonlinear integrable differential equation, and each solution of this equation determines a background geometry on which, for any Lie group $G$, an integrable gauge theory is defined. In four dimensions, the geometry is selfdual conformal geometry and the gauge theory is selfdual Yang-Mills theory, while the lower-dimensional structures are nondegenerate (i.e., non-null) reductions of this. Any solution of the gauge theory on a $k$-dimensional geometry, such that the gauge group $H$ acts transitively on an $\ell$-manifold, determines a $(k+\ell)$-dimensional geometry ($k+\ell\leqslant4$) fibering over the $k$-dimensional geometry with $H$ as a structure group. In the case of an $\ell$-dimensional group $H$ acting on itself by the regular representation, all $(k+\ell)$-dimensional geometries with symmetry group $H$ are locally obtained in this way. This framework unifies and extends known results about dimensional reductions of selfdual conformal geometry and the selfdual Yang-Mills equation, and provides a rich supply of constructive methods. In one dimension, generalized Nahm equations provide a uniform description of four pole isomonodromic deformation problems, and may be related to the ${\rm SU}(\infty)$ Toda and dKP equations via a hodograph transformation. In two dimensions, the ${\rm Diff}(S^1)$ Hitchin equation is shown to be equivalent to the hyperCR Einstein-Weyl equation, while the ${\rm SDiff}(\Sigma^2)$ Hitchin equation leads to a Euclidean analogue of Plebanski's heavenly equations.Comment: for Progress in Twistor Theory, SIGM