Related papers: "Anomaly" in n=infinity Alday-Maldacena Duality fo…
Alday-Maldacena conjecture is that the area A_P of the minimal surface in AdS_5 space with a boundary P, located in Euclidean space at infinity of AdS_5, coincides with a double integral D_P along P, the Abelian Wilson average in an…
We further develop the formalism of arXiv:0712.0159 for approximate solution of Nambu-Goto (NG) equations with polygon conditions in AdS backgrounds, needed in modern studies of the string/gauge duality. Inscribed circle condition is…
We describe an algebro-geometric construction of polygon-bounded minimal surfaces in ADS_5, based on consideration of what we call the "boundary ring" of polynomials. The first non-trivial example of the Nambu-Goto (NG) solutions for…
A short summary of approximate approach to the study of minimal surfaces in AdS, based on solving Nambu-Goto equations iteratively. Today, after partial denunciation of the BDS conjecture, this looks like the only constructive approach to…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…
A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…
In this thesis, we investigate hidden symmetries for the Maldacena-Wilson loop in N=4 super Yang-Mills theory, mainly focusing on its strong-coupling description as a minimal surface in $AdS_5$. In the discussion of the symmetry structure…
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to…
We study anomalies of non-invertible duality symmetries in both 2d and 4d, employing the tool of the Symmetry TFT. In the 2d case we rephrase the known obstruction theory for the Tambara-Yamagami fusion category in a way easily…
We study the low energy behaviour of N=(2,2) supersymmetric gauge theories in 1+1 dimensions, with orthogonal and symplectic gauge groups and matters in the fundamental representation. We observe supersymmetry breaking in super-Yang-Mills…
In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the…
Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror…
We further analyze a recent perturbative two-loop calculation of the expectation value of two axi-symmetric circular Maldacena-Wilson loops in N=4 gauge theory. Firstly, it is demonstrated how to adapt the previous calculation of…
We introduce an analogue of Payne's nodal line conjecture, which asserts that the nodal (zero) set of any eigenfunction associated with the second eigenvalue of the Dirichlet Laplacian on a bounded planar domain should reach the boundary of…
Calculations of the two-loop $\beta$-function for N=1 supersymmetric electrodynamics are compared for regularizations by higher derivatives and by the dimensional reduction. The renormalized effective action are found to be the same for…
We compute the complete bulk one-loop contribution to the Weyl anomaly of the boundary theory for IIB Supergravity compactified on $ AdS_5\times S^5$. The result, that $\delta {\cal A}=(E+I)/(2\pi^2)$, reproduces the subleading term in the…
We extend the classification of supersymmetric locally AdS$_3$ geometries, beyond BTZ black holes, to the Banados geometries, noting that supersymmetries are in one-to-one correspondence with solutions to the Hill differential condition. We…
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…
Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy, where the problem of minimum variance estimation is shown to be dual to a…
Irregular conformal block is motivated by the Argyres-Douglas type of N=2 super conformal gauge theory. We investigate the classical/NS limit of the irregular conformal block using spectral curve on a Riemann surface with irregular…