One-point Functions in AdS/dCFT from Matrix Product States

TL;DR

This paper derives a determinant formula for one-point functions in defect CFTs dual to D3-D5 brane systems, linking Bethe states and matrix product states, and explores their relation via transfer matrices and Baxter Q-operators.

Contribution

It provides a closed, determinant expression for one-point functions for any flux parameter k, connecting matrix product states for different k values and relating them through transfer matrices and Q-operators.

Findings

Determinant formula valid for all k values.

Recursive relations between matrix product states for different k.

Evidence of relations between matrix product states via Baxter's Q-operators.

Abstract

One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k=2 result times a k-dependent prefactor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k=2 and k=3 respectively. We furthermore find evidence that the matrix product states for k=2 and k=3 are related via a ratio of Baxter's Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.