相关论文: N=4 Multi-Particle Mechanics, WDVV Equation and Ro…

In this paper we consider the algebra of upper triangular matrices UT$_n(F)$, endowed with a $\mathbb{Z}_2$-grading (superalgebra) and equipped with a superinvolution. These structures naturally arise in the context of Lie and Jordan…

We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.

We first recall Solomon's relations for Welschinger's invariants counting real curves in real symplectic fourfolds, announced in \cite{Jake2} and established in \cite{RealWDVV}, and the WDVV-style relations for Welschinger's invariants…

We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for…

We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a…

The V-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of V-systems are known but their classification is an open problem. We…

It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems. We extend some of these results to arbitrary dimension $N$ and arbitrary scalar product $\eta$. In particular, we show that…

We study the necessary conditions for preserving N=(4,4) supersymmetry on curved 2d backgrounds, following the strategy of Dumitrescu, Festuccia, and Seiberg. We derive the transformation laws and invariant action for off-shell Abelian…

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

We propose a unified superfield formulation of N=4 off-shell supermultiplets in one spacetime dimension using the standard N=4 superspace. The main idea of our approach is a "gluing" together of two linear supermultiplets along their…

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to…

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for…

In this first of two papers, we explain in detail the simplest example of a broader set of relations between apparently very different theories. Our example relates $\mathfrak{su}(2)$ $\mathcal{N}=4$ super Yang-Mills (SYM) to a theory we…

We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…

We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such…

The issue of constructing an N=4 superconformal mechanics in one dimension is reconsidered with a special emphasis put on the realizations of the su(2)-subalgebra in the full su(1,1|2)-superalgebra. New dynamical realizations of su(1,1|2)…

We pursue a uniform quantization of all twists of 4-dimensional N = 4 supersymmetric Yang-Mills theory, using the BV formalism, and we explore consequences for factorization algebras of observables. Our central result is the construction of…

A new class of deformation of the matrix model of M-theory is considered. The deformation is analogous to the so-called $\b$-deformation of $D=3+1$, $\mN=4$ Super Yang-Mills theory, which preserves the conformal symmetry. It is shown that…

The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory…

The prepotential $F(a_i)$, defining the low-energy effective action of the $SU(N)$ ${\cal N}=2$ SUSY Yang-Mills theories, satisfies an enlarged set of the WDVV-like equations $F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$ for any triple $i,j,k =…