Related papers: Solvable spectral problems from 2d CFT and N=2 gau…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…
In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with…
Different cases of sequences of the Laplace Transformations for the 2D Schrodinger operator in the periodic magnetic field and electric potential are considered. They lead to the exactly solvable operators with nonstandard spectral…
We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of $2\times 2$ linear systems (Riemann-Hilbert correspondence). Our technique applies…
In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
We consider a wide class of two-dimensional models as gauge theories, Gross-Neveu model, $O(N)$ and $CP^{N-1}$-like models using a formalism based on the introduction of bilocal fields that permits to perform easily the large-N expansion of…
Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
We find new $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ dualities through the twisted compactifications of 4d supersymmetric theories on $S^2$. Our findings include dualities for both $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,2)$ non-Abelian…
Second-order conformal quantum superintegrable systems in 2 dimensions are Laplace equations on a manifold with an added scalar potential and $3$ independent 2nd order conformal symmetry operators. They encode all the information about 2D…
We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin…
We show that all two-dimensional conformal field theories possess a hidden sl(2,R) affine symmetry. More precisely, we add appropriate ghost fields to an arbitrary CFT, and we use them to construct the currents of sl(2,R). We then define a…
We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy…
We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple Higgs fields in the adjoint representation, that can be mapped to cuprate systems in…
We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional…
We report an exact solution of 2- and 3-point functions of chiral primary fields in SU(2) N=2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are non-trivial functions of the gauge…
The anomalous dimensions of operators in the purely gluonic SU(2,1|2) sector of any planar conformal N=2 theory can be read off from the N=4 SYM results by replacing the N=4 coupling constant by an interpolating function of the N=2 coupling…
In this paper we study 3d $\mathcal{N}=2$ $SU(N)$ confining gauge theories with a matter field in the rank-two index symmetric representation. The models found here are obtained from the application of the duplication formula for hyperbolic…