Related papers: Harmonicity in N=4 supersymmetry and its quantum a…
It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar…
We perform an $su(2)$ Hamiltonian reduction in the bosonic sector of the $su(2)$-invariant action for two free $(4,4,0)$ supermultiplets. As a result, we get the five dimensional \Nf supersymmetric mechanics describing the motion of an…
Possible short and semi-short representations for $\N=2$ and $\N=4$ superconformal symmetry in four dimensions are discussed. For $\N=4$ the well known short supermultiplets whose lowest dimension conformal primary operators correspond to…
Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the…
We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and…
We study the tension of vortices in N=2 SQCD broken to N=1 by a superpotential W(\Phi), in color-flavor locked vacua. The tension can be written as T = T_{BPS} + T_{non BPS}. The BPS tension is equal to 4\pi|\T| where we call \T the…
The N=4 superconformal algebra is derived from the symmetry transformations of fields in the N=4 SYM action in D=4. We use a Majorana-Weyl spinor in D=10 instead of four Weyl spinors in D=4. This makes it transparent to relate generators of…
Using the harmonic superspace approach we construct the superconformal harmonic action for $\mathcal{N}=2$ Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials $h^{++\alpha\dot{\alpha}},…
We elaborate on a novel model of N=4 supersymmetric mechanics with extra spin variables. A dynamical linear (1,4,3) multiplet is coupled to a "semi-dynamical" linear (3,4,1) multiplet representing spin degrees of freedom in a Wess-Zumino…
Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity,…
This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…
We develop semiclassical methods to analyze the spectrum of BPS monopole operators for superconformal field theories in three dimensions with N=2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical…
Given an N=2 supersymmetric field theory in four dimensions, its dimensional reduction on S^1 is a sigma model with hyperkahler target space M. We describe a canonical line bundle V on M, equipped with a hyperholomorphic connection. The…
We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic…
We present a systematic analysis of the N=6 superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SU(4) tensor $W^i_j$ which is a function of the matter fields…
The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanical harmonic oscillator carry over to the study of more…
In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…
We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in terms of…
We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for…