Diego H. Correa

The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

A bstractWe derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L = 0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.

An exact formula for the radiation of a moving quark in \mathcal{N} = 4 super Yang Mills

A bstractWe derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in

The cusp anomalous dimension at three loops and beyond

\mathcal{N} = 4

Reflecting magnons from D7 and D5 branes

super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.

Comments on the boundary scattering phase

We derive an analytic formula at three loops for the cusp anomalous dimension Γcusp(ϕ) in

Geometry and topology of bubble solutions from gauge theory

\mathcal{N} = {4}

Strings in AdS 4 × ℂℙ3, Wilson loops in \( \mathcal{N} \) = 6 super Chern-Simons-matter and bremsstrahlung functions

super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the corresponding three loops quark anti-quark potential. Our result also determines a considerable part of the three- loop cusp anomalous dimension in QCD. Finally, we consider a limit in which only ladder diagrams contribute to physical observables. In that limit, a precise agreement with strong coupling is observed.

Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in AdS5 × S 5 . In each case we consider two possible orientations for the vacuum state. We show that symmetry arguments are sufficient to determine the reflection matrices up to at most two unknown functions. The D7 reflection matrices obey the boundary Yang Baxter-Equation. This is automatic for one vacuum orientation, and requires a natural choice of ratio between two unknowns for the other. In contrast, the D5 reflection matrices do not obey the boundary Yang Baxter-Equation. In both cases we show consistency with the existent weak and strong coupling results.

Asymptotic Bethe equations for open boundaries in planar AdS/CFT

We present a simple solution to the crossing equation for an open string worldsheet reflection matrix, with boundaries preserving a SU(1|2)2 residual symmetry, which constrains the boundary dressing factor. In addition, we also propose an analogous crossing equation for the dressing factor where extra boundary degrees of freedom preserve a SU(2|2)2 residual symmetry.

Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

We study how geometrical and topological aspects of certain 1 -BPS type IIB supergravity solutions are captured by the N = 4 Super Yang-Mills gauge theory in the AdS/CFT context. The type IIB solutions are completely characterized by arbitrary droplets in a plane and we consider, in particular, concentric droplets. We probe the dual 1 -BPS operators of the gauge theory with single traces and extract their one-loop anomalous dimensions. The action of the one-loop dilatation operator can be reformulated as the Hamiltonian of a bosonic lattice. The operators defining the Hamiltonian encode the topology of the droplet. The axial symmetry of the droplets turns out to be essential for obtaining the spectrum of the Hamiltonians. In appropriate BMN limits, the near-BPS spectrum reproduces the spectrum of near-BPS string excitations propagating along each individual edge of the droplet of the dual geometric background. We also study semiclassical regimes for the Hamiltonians. We show that for droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.