Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries

Abstract

We consider the integrable open-chain transfer matrix corresponding to a Y = 0 brane at one boundary, and a Y θ = 0 brane (rotated with the respect to the former by an angle θ) at the other boundary. We determine the exact eigenvalues of this transfer matrix in terms of solutions of a corresponding set of Bethe equations.

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

“…By contrast, the analysis of determinant operators is much less developed. The spectrum of small deformations of determinant operators was analyzed using various approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] including integrability [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. However, not much work has been done on correlation functions 3 except in the protected BPS sector [37][38][39] and in the free field limit, where various interesting structures were found using algebraic [40], combinatorial [41][42][43] and coherent state [44] approaches.…”

“…where v|v is the Gaudin norm for the nested Bethe roots on the right wing while the induced Gaudin determinant detG − is given by 33) which can be computed by first solving for v and then evaluating the derivatives. As a result, we find that the Gaudin norms for the nested Bethe roots cancel in the ratio, det…”

Massless AdS 2 scattering and Bethe ansatz

“…A variety of approaches have been developed in the literature to overcome such problems, starting with Baxter's original method of functional relations. Recently, [70][71][72] successfully applied this strategy to non-diagonal boundary problems, which suffer from the same issue (see also e.g. [73] for one particular example out of the vast related literature).…”

Wrapping corrections for non-diagonal boundaries in AdS/CFT

“…. , w M } are 2 We compensate for the fact that the definition of g in [16] differs by a factor 2 from the one used here.…”