We consider the problem of resumming the perturbative expansions for anomalous dimensions of low twist, non-BPS operators in four dimensional N=4 supersymmetric Yang-Mills theories. The requirement of S-duality invariance imposes considerable restrictions on any such resummation. We introduce several prescriptions that produce interpolating functions on the upper half plane that are compatible with a subgroup of the full duality group. These lead to predictions for the anomalous dimensions at all points in the fundamental domain of the complex gauge coupling, and in particular at the duality-invariant values τ=i and τ=exp(iπ/3). For low-rank gauge groups, the predictions are compatible with the bounds derived by conformal bootstrap methods for these anomalous dimensions; within numerical errors, they are in good agreement with the conjecture that said bounds are saturated at a duality-invariant point. We also find that the anomalous dimensions of the lowest twist operators lie within an extremely narrow window around a straight line as we vary the moduli of the theory over the two dimensional fundamental domain.
We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat-kernel to all order in a homogeneous background and to quadratic order in perturbations, giving a closed expression for the corresponding effective action in $D=4$. In the dynamical case, we analyze the pair production caused by a harmonic pertu…
We present the technique for resummation of flux tube excitations series arising in pentagon operator expansion program for polygonal Wilson loops in N=4 SYM. Here we restrict ourselves with contributions of one-particle effective states and consider as a particular example NMHV 6 particle amplitude at one-loop. The presented technique is also applicable at higher loops for one effective particle contributions and has the potential for generalization for contributions with more effective particles.
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the "rapidity identity operators", that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $\mathcal{N}$=4 super-Yang-Mills. These logar…
We discuss the resummation procedure of the superpotential in 4d $\mathcal{N}=2$ SYM theory without matter from the point of view of 2d Liouville conformal field theory, utilizing the AGT correspondence. We identify contributions of different descendants of the intermediate state, defining a conformal block in CFT, to the superpotential and answer the question, which descendants are responsible for the appearance of the branch cuts in the superpotential.
We revisit the multi-loop structure of the anomalous-dimension matrix governing the infrared divergences of massless $n$-particle scattering amplitudes in non-abelian gauge theories. In particular, we derive its most general form at four-loop order, significantly simplifying corresponding expressions given previously. By carefully reevaluating the constraints imposed by two-particle collinear limits, we find that at four-loop order color structures involving $d_R^{abcd}$, the symmetrized trace of four group generators, appear along with cusp logarithms $\ln[μ^2/(-s_{ij})]$. As a consequence, n…
