Related papers: Minimal area surfaces in AdS$_3$ through integrabi…
We construct constant mean curvature surfaces of the general finite-gap type in AdS_3. The special case with zero mean curvature gives minimal surfaces relevant for the study of Wilson loops and gluon scattering amplitudes in N=4 super…
We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model.…
In this paper, minimal surface in $q$-deformed $AdS_5\times S^5$ with boundary a cusp is studied in detail. This minimal surface is dual to cusped Wilson loop in the dual field theory. We found that the area of the minimal surface has both…
We consider compact connected minimal surfaces, with a pair of boundary curves (not necessarily convex) in distinct planes, that have least-area amongst all orientable surfaces with the same boundary. When the planes containing these two…
Non-linear sigma models defined on symmetric target spaces have a wide set of applications in modern physics, including the description of string propagation in symmetric spaces, such as AdS or dS, or minimal surfaces in hyperbolic spaces.…
Based on an extension of the holographic principle to superspace, we provide a strong-coupling description of smooth super Wilson loops in terms of minimal surfaces of the $AdS_5 \times S^5$ superstring. We employ the classical…
The Ryu-Takayanagi conjecture connects the entanglement entropy in the boundary CFT to the area of open co-dimension two minimal surfaces in the bulk. Especially in AdS(4), the latter are two-dimensional surfaces, and, thus, solutions of a…
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…
We study the null-polygonal minimal surfaces in AdS_4, which correspond to the gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the…
We describe new solutions for open string moving in AdS_5 and ending in the boundary, namely dual to Wilson loops in N=4 SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are BPS…
We prove that if $f_g: (\Sigma,g) \rightarrow (\mb{S}^{2+p},\tg)$ is a smooth minimal isometric embedding of a Riemannian surface $(\Sigma,g)$, and $[0,1]\ni t \rightarrow g_t$ is a path of area preserving conformal deformations of $g$ on…
We address the problem of computing scattering amplitudes related to the correlation function of two Wilson lines and/or loops elongated along light-cone directions in strongly coupled gauge theories. Using the AdS/CFT correspondence in the…
We revisit the computation of the 1-loop string correction to the "latitude" minimal surface in $AdS_5 \times S^5$ representing 1/4 BPS Wilson loop in planar $\cal N$=4 SYM theory previously addressed in arXiv:1512.00841 and…
We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS$_5$. The Lax pair for the reduced theory is found, and written entirely in terms of the $A_3=D_3$ root system, generalizing the $B_2$ affine Toda system which…
We study path-integrals over reparametrizations of the world-sheet boundary. Such integrals arise when string propagates between fixed space-time contours. In gauge/string duality they are needed to describe gauge theory Wilson loops. We…
This article explains a program to study complete and properly embedded minimal surfaces in $\mathbb{R}^3$ developed jointly with W.H. Meeks and A. Ros in the last three decades. It follows closely the structure of my invited ICM talk with…
In this paper we present an algorithm to reduce the area of a surface spanned by a finite number of boundary curves by initiating a variational improvement in the surface. The ansatz we suggest consists of original surface plus a…
We develop the method based on $ \mathcal{B} $-automorphism for finding new lattice integrable models with various dimensions of local Hilbert spaces. We initiate the technique by implementing it to the two-dimensional models and resolve…
In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in $\mathbb{R}^{2 + n}$. We prove regularity of $W^{1,2}$ solutions and a compactness result for approximate solutions of…
We investigate elliptical Wilson loops in ${\cal N}=4$ Super Yang--Mills theory at weak and strong coupling for small values of the eccentricity. We obtain analytical results for the vacuum expectation value of the Wilson loop in the form…