A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevan...

The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characteristic polynomial. A condition is derived using certain known facts about matrix minors and its chara...

We consider the model of random surfaces with extrinsic curvature term embedded into 3d Euclidean lattice Z 3. On a 3d Euclidean lattice it has equivalent representation in terms of transfer matrix K(Q i , Q f), which describes the propagation of loops Q. We study the spectrum of the transfer matrix K(Q i , Q f) on finite dimensional lattices. The renormalisation group technique is used to inve...

We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the SU(N) adjoint representation to other matrix models, namely the free SO(N) and Sp(N) adjoint models as well as the free U(N)×U(M) bi-fundamental and O(N)×O(M) bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we comp...

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann’s version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and li...