Beyond cusp anomalous dimension from integrability in SYM4_4

We study the first sub-leading correction $O((\ln s)^0)$ to the cusp anomalous dimension in the high spin expansion of finite twist operators in ${\cal N}=4$ SYM theory. This term is still governed by a linear integral equation which we study in the weak and strong coupling regimes. In the strong coupling regime we find agreement with the string theory computationsComment: 5 pages, contribution to the proceedings of the workshop Diffraction 2010, Otranto, 10th-15th September, talk given by M.Rossi; v2: references adde

On the finite size corrections of anti-ferromagnetic anomalous dimensions in N=4{\cal N}=4 SYM

Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and immediately lower anomalous dimensions of scalar operators in ${\cal N}=4$ SYM. In specific, multi-loop corrections are computed in the SU(2) operator subspace, whereas in the general SO(6) case only one loop calculations have been finalised. In these cases, the leading finite size corrections are given by means of explicit formul\ae and compared with the exact numerical evaluation. In addition, the method here proposed is quite general and especially suitable for numerical evaluations.Comment: 38 pages, Latex revised version: draft formulae indicator deleted, one reference added, typos corrected, few minor text modification

Decay of particles above threshold in the Ising field theory with magnetic field

The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles A_i (i=1,...,8) with different masses. The heaviest five lie above threshold and owe their stability to integrability. We use form factor perturbation theory to compute the decay widths of the first two particles above threshold when integrability is broken by a small deviation from the critical temperature. The lifetime ratio t_4/t_5 is found to be 0.233; the particle A_5 decays at 47% in the channel A_1A_1 and for the remaining fraction in the channel A_1A_2. The increase of the lifetime with the mass, a feature which can be expected in two dimensions from phase space considerations, is in this model further enhanced by the dynamics.Comment: 15 pages, 5 figures; minor typos correcte

On the magnetic perturbation of the Ising model on the sphere

In this letter we will extend the analysis given by Al. Zamolodchikov for the scaling Yang-Lee model on the sphere to the Ising model in a magnetic field. A numerical study of the partition function and of the vacuum expectation values (VEV) is done by using the truncated conformal space (TCS) approach. Our results strongly suggest that the partition function is an entire function of the coupling constant.Comment: 8 pages, 1 figure, revised version, references adde

Study of the flux tube thickness in 3d LGT's by means of 2d spin models

We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the correlation function in the two-dimensional spin model with Z_2 global symmetry, (i.e. the 2d Ising model) in the high-temperature phase. Using the form factor approach we obtain an explicit expression for this function and from it we infer the behaviour of the flux density of the original (2+1)d LGT. Remarkably enough the result we obtain for the flux tube thickness agrees (a part from an overall normalization) with the effective string prediction for the same quantity

Integrable structures in LGTs near the deconfinement transition

In this contribution we review some recent results about the emergence of 2D integrable systems in 3D Lattice Gauge Theories near the deconfinement transition. We focus on some concrete examples involving the flux tube thickness, the ratio of k-string tensions and Polyakov loops correlators in various models.Comment: 8 pages, Poster contribution to the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin