Related papers: Large spin corrections in ${\cal N}=4$ SYM sl(2): …
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$, and this…
In this paper it is argued that the central charge extension of the Coulomb branch of ${\cal N}=4 $ SYM theory appears as a limit of Beisert's central charge extension of the planar ${\cal N}=4 $ spin chain in the presence of boundaries.…
We give a lattice theory treatment of certain one and two dimensional quantum field theories. In one dimension we construct a combinatorial version of a non-trivial field theory on the circle which is of some independent interest in itself…
In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this…
We investigate the problem of entire solutions for a class of fourth order, dilation invariant, semilinear elliptic equations with power-type weights and with subcritical or critical growth in the nonlinear term. These equations define non…
A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N=(8,8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar…
Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized ${\cal N}=4$ SYM theory, are considered in some detail. Duality between…
A world-sheet sigma model approach is applied to string theories dual to four-dimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory…
Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…
We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the $sl(2)$ sector of planar ${\cal N}=4$ SYM. In…
We show that the equations of motion for (free) integer higher spin gauge fields can be formulated as twisted self-duality conditions on the higher spin curvatures of the spin-$s$ field and its dual. We focus on the case of four spacetime…
We study $(1+1)$-dimensional $SU(N)$ spin systems in the presence of the global $SU(N)$ rotation and lattice translation symmetries. By matching the mixed anomaly of the $PSU(N)\times\mathbb{Z}$ symmetry in the continuum limit, we identify…
Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on…
The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$.…
In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic…
We consider the Renyi entropies S_n in one-dimensional massive integrable models diagonalizable by means of corner transfer matrices (as Heisenberg and Ising spin chains). By means of explicit examples and using the relation of corner…
We present a comprehensive \textit{ab initio} analysis of the spin-charge correlations at the Tl/Si(111) surface, where the spin-orbit interaction is so strong that a detailed treatment of the non-collinear electron spin appears decisive…
We study the 4-th Binder cumulant on $4\times{N_\sigma}^3$ lattices for a pure SU(2) gauge theory. We use 20 data points for a sequence of ${N_\sigma}$ in $\beta$ intervals shrinking when ${N_\sigma}$ increases, in order to reduce the…
Recently it has been shown how a topologically twisted version of ${\cal N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are…
We revisit unitary representation of centrally extended (2 | 2) excitation superalgebra. We find most generally that `pseudo-momentum', not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain.…