Electromagnetic form factors from the fifth dimension

We analyse various $U(1)_{EM}$ form factors of mesons at strong coupling in an $\mathcal{N}=2$ flavored version of $\mathcal{N}=4$ $SYM$ which becomes conformal in the UV. The quark mass breaks the conformal symmetry in the IR and generates a mass gap. In the appropriate limit, the gravity dual is described in terms of probe $D7$-branes in $AdS_5\times S^5$. By studying the $D7$ fluctuations we find the suitable terms in a "meson effective theory" which allow us to compute the desired form factors, namely the $\gamma\pi\rho$ and $\gamma f_0\rho$ transition form factors. At large $q^2$ we find perfect agreement with the naive parton model counting, which is a consequence of the conformal nature of both QCD and our model in the UV. By using the same tools, we can compute the $\gamma^*\gamma^*\pi$ form factor. However this channel is more subtle and comparisons to the QCD result are more involved.Comment: 34 pages, 6 figures, pdflatex. References and clarifications adde

Thermal correlation functions in CFT and factorization

We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in $d$ dimensions in terms of the $c$-anomaly coefficient. By including $\alpha'$ corrections to the black brane background, one can reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula, which reduces to the expected expressions in different limits. When the dimensions satisfy $\Delta_i= \Delta_j+ \Delta_k$, the thermal 3-point function satisfies a factorization property. We argue that in $d>2$ factorization is a reflection of the semiclassical regime.Comment: 26 page

Defects in scalar field theories, RG flows and Dimensional Disentangling

We consider defect operators in scalar field theories in dimensions $d=4-\epsilon$ and $d=6-\epsilon$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the defect couplings go to infinity, the bulk theory becomes classical and the quantum defect theory can be solved order by order in perturbation theory. We compute the defect $\beta$ functions to two loops and study the Renormalization Group flows. The defect fixed points can move and merge, leading to fixed point annihilation; and they exhibit a remarkable factorization property where the $\epsilon$-dependence gets disentangled from the coupling dependence.Comment: 26 pages, 7 figure

Nekrasov-Shatashvili limit of the 5D superconformal index

C. P. is supported by the Royal Society through a University Research Fellowship. A. P. and D. R. G. are partly supported by the Spanish Government Grant No. MINECO-13-FPA2012-35043-C02-02. In addition, they acknowledge financial support from the Ramon y Cajal Grant No. RYC-2011-07593 as well as the EU CIG Grant No. UE-14-GT5LD2013-618459. The work of A. P. is funded by the Asturian Government SEVERO OCHOA Grant No. BP14-003

Exact solutions of an elliptic Calogero--Sutherland model

A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and the lowest excitations are calculated explicitly for N=2.Comment: 4 pages, 3 figures, typeset with RevTeX 4b3 and AMS-LaTe

RG Flows and Stability in Defect Field Theories

We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the defect coupling. We compute $\beta$-functions up to four loops and find that fixed points satisfy dimensional disentanglement -- i.e. their dependence on the space dimension is factorized from the coupling dependence -- and discuss some physical implications. We also give an alternative derivation of the $\beta$ functions by computing systematic logarithmic corrections to the Coulomb potential. In this natural scheme, $\beta$ functions turn out to be a gradient of a `Hamiltonian' function ${\cal H}$. We also obtain closed formulas for the dimension of scalar operators and show that instabilities do not occur for potentials bounded from below. The same formulas are reproduced using Rigid Holography.Comment: 35 pages, 1 figure; v2: added reference

Dielectric branes in non-trivial backgrounds

We present a procedure to evaluate the action for dielectric branes in non-trivial backgrounds. These backgrounds must be capable to be taken into a Kaluza-Klein form, with some non-zero wrapping factor. We derive the way this wrapping factor is gauged away. Examples of this are AdS_5xS^5 and AdS_3xS^3xT^4, where we perform the construction of different stable systems, which stability relies in its dielectric character.Comment: 14 pages, published versio

NR-SLAM: Non-Rigid Monocular SLAM

In this paper we present NR-SLAM, a novel non-rigid monocular SLAM system founded on the combination of a Dynamic Deformation Graph with a Visco-Elastic deformation model. The former enables our system to represent the dynamics of the deforming environment as the camera explores, while the later allows us to model general deformations in a simple way. The presented system is able to automatically initialize and extend a map modeled by a sparse point cloud in deforming environments, that is refined with a sliding-window Deformable Bundle Adjustment. This map serves as base for the estimation of the camera motion and deformation and enables us to represent arbitrary surface topologies, overcoming the limitations of previous methods. To assess the performance of our system in challenging deforming scenarios, we evaluate it in several representative medical datasets. In our experiments, NR-SLAM outperforms previous deformable SLAM systems, achieving millimeter reconstruction accuracy and bringing automated medical intervention closer. For the benefit of the community, we make the source code public.Comment: 12 pages, 7 figures, submited to the IEEE Transactions on Robotics (T-RO