Related papers: Nested coordinate Bethe wavefunctions from the Bet…
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…
Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge…
These notes arose from three lectures presented at the Summer School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter" held in Myczkowce, Poland, on September 11-18, 2002. We review rigged configurations and…
The scalar products, form factors and correlation functions of the XXZ spin chain with twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous $T-Q$ relation and the Bethe states constructed via the off-diagonal…
In recent years, charge-channel orders in strongly correlated metals have attracted great attention. Famous examples are the electronic nematic orders in cuprates and iron-based superconductors, and Star-of-David order in kagome metals.…
Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a…
We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…
In this thesis we present some computations made in both sides of the AdS/CFT holographic correspondence using the integrability of both theories. Regarding the string theory side, this thesis is focused in the computation of the dispersion…
We derive an infinite set of recursion formulae for Nekrasov instanton partition function for linear quiver U(N) supersymmetric gauge theories in 4D. They have a structure of a deformed version of W_{1+\infty} algebra which is called SH^c…
The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is…
We study the $\mathfrak{gl}_{m|n}$ XXX spin chains defined on tensor products of highest $\mathfrak{gl}_{m|n}$-modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding…
In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…
We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in $\mathcal{N}=2$ gauge theories on ALE spaces based on quiver varieties and the minimal resolution $X_k$ of…
The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…
We briefly review Bethe Ansatz solutions of the integrable open spin-1/2 XXZ quantum spin chain derived from functional relations obeyed by the transfer matrix at roots of unity.
The AGT conjecture relates \mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the…
With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer…
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa…
Using recursive relations satisfied by Nekrasov partition functions and by irregular conformal blocks we prove the AGT correspondence in the case of N=2 superconformal SU(2) quiver gauge theories with N_f = 0,1,2 antifundamental…
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…