Related papers: Generalized Bethe expansions of superconformal ind…
We study the Bethe Ansatz formula for the superconformal index, in the case of 4d $\mathcal{N}=4$ super-Yang-Mills with gauge group $SU(N)$. We observe that not all solutions to the Bethe Ansatz Equations (BAEs) contribute to the index, and…
Inspired by recent work by Closset, Kim and Willett, we derive a new formula for the superconformal (or supersymmetric) index of 4d N=1 theories. Such a formula is a finite sum, over the solution set of certain transcendental equations that…
We investigate the Bethe-Ansatz (BA) approach to the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills with SU($N$) gauge group in the context of finite rank, $N$. We explicitly explore the role of the various types of…
We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the…
Supersymmetric partition function of $\mathcal N=1$ superconformal theories on $S^1_{\beta} \times S^3$ is related to the superconformal index receiving contributions from short representations. The leading coefficients in the small $\beta$…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…
Applying the approach based on the equation for the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the incomplete Beta functions. Several expansions in terms of the Appell generalized…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we…
We study the superconformal index of $\mathcal N=1$ quiver theories at large-$N$ for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are…
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…
We consider the Bethe Ansatz Equations for orbifolds of N =4 SYM w.r.t. an arbitrary discrete group. Techniques used for the Abelian orbifolds can be extended to the generic non-Abelian case with minor modifications. We show how to make a…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
The superconformal index of the $\mathcal{N}=4$ SU(N) supersymmetric Yang-Mills theory counts the 1/16-BPS states in this theory, and has been used via the AdS/CFT correspondence to count black hole microstates of 1/16-BPS black holes. On…
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…
The general expression for the local matrix of a quantum chain $L(\theta)$ with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the fist kind. The coefficients of different…
We study the expansion near roots of unity of the superconformal index of 4d $SU(N)$ $\mathcal{N}=4$ SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the…
A class of integrable boundary terms for the eight-state supersymmtric $U$ model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz…