Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for nonlinear and non-Gaussia...

The construction of a relativistic quantum field is still an open problem for fields in spacetime dimension d ≥ 4. The conceptual difficulty that sometimes led to fear an incompatibility between nontrivial quantum systems and special relativity has however been solved in the case of dimension d = 2, 3 although, so far, has not influenced the corresponding debate on the foundations of quantum me...

This review concentrates on progress in lattice QCD during the last two years and, particularly, its impact on phenomenology. The two main technical developments have been successful implementations of lattice actions with exact chiral symmetry, and results from simulations with two light dynamical flavours which provide quantitative estimates of quenching effects for some quantities. Results a...

We present one loop boundary reflection matrix for d (1) 4 Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be ‘n...

These notes were prepared as a support for a talk at the graduate workshop ”Supersymmetric Field Theories and Their Mathematical Implications” held in March 2012 at the Simons Center in Stony Brook. They are essentially cut out of [1], from which nearly all the material is taken, with a little rearrangement. To the reader looking for a richer exposition we definitely suggest the excellent sourc...

TheR-matrix of the Uq ( d (3) 4 ) algebra is constructed in the 8-dimensional fundamental representation. Using this result, an exact S-matrix is conjectured for the imaginary coupled g (1) 2 affine Toda field theory, the structure of which is found to be very similar to the previously investigated S-matrix of d (3) 4 Toda theory. It is shown that this Smatrix is consistent with the results for...

In this paper we define and study the moduli space of metric-graphflows in a manifold M . This is a space of smooth maps from a finite graph to M , which, when restricted to each edge, is a gradient flow line of a smooth (and generically Morse) function on M . Using the model of Gromov-Witten theory, with this moduli space replacing the space of stable holomorphic curves in a symplectic manifol...

This is a brief review of vacuum string field theory, a new approach to open string field theory based on the stable vacuum of the tachyon. We discuss the sliver state explaining its role as a projector in the space of half-string functionals. We review the construction of D-brane solutions in vacuum string field theory, both in the algebraic approach and in the more general geometrical approac...

We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been dis...

T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type IIB * theory and the IIB theory to a type IIA * theory. The type II * theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effe...