Integrable boundary states in D3-D5 dCFT: beyond scalars

Abstract

A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this setup map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k = 1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult for k > 1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.

Duality relations for overlaps of integrable boundary states in AdS/dCFT

“…(2.26). The overlaps with VBS 0 are precisely those that appear in the Bethe ansatz description of the one-point functions in the simplest domain-wall dCFT [12].…”

“…The overlap formula in this form was first derived for the Néel state (|VBS 1 ) in the Heisenberg model [45][46][47] by exploiting connections [48] to the six-vertex partition function with specific boundary conditions [49]. As for higher-rank spin chains, rigorous derivations JHEP09(2021)004 are seldom available, but many overlap formulas were conjectured [12,26,27,30] or deduced from scattering theory [10,13,36], coordinate Bethe ansatz [50] and TBA [44].…”

“…We will address a class of duality relations which rather pertain to the microscopical level. These are dualities which characterize the integrable super spin chain underlying the AdS/CFT correspondence [3][4][5][6] and its associated integrable boundary states describing the D3-D5 defect set-up [7][8][9][10][11][12][13].…”

“…Here we shall address the simplest possible correlation functions of N = 4 SYM namely one-point JHEP09(2021)004 functions of the integrable D3-D5 probe brane set-up. These one-point functions can be expressed as overlaps between Bethe eigenstates and integrable boundary states in the form of either matrix product states or valence bond states [7,8,12].…”

“…Closed expressions found for these overlaps [7,8,12,26,27] have lead to a derivation of an asymptotic all-loop formula for the one-point functions in question [9][10][11][12][13], as well as for three-point functions involving a single trace operator and two giant gravitons both in N = 4 SYM [28] and in ABJM theory [29,30], and have sparked novel developments in statistical physics [31][32][33][34] where the overlaps are of relevance for the study of quantum quenches. The overlap formulas contain a universal part expressed in terms of the super determinant of the Gaudin matrix [35] of the Bethe state in question and a dynamical factor depending on the boundary state and being expressible as a product of Q-functions.…”