One-point functions in $\beta$-deformed N = 4 SYM with defect

TL;DR

This paper extends the study of one-point functions in N=4 SYM with a defect to the $eta$-deformed version, expressing vacuum expectation values as overlaps in a twisted spin-chain and analyzing their properties.

Contribution

It introduces a $eta$-deformed framework for one-point functions, showing how deformation affects the integrability and overlap calculations compared to the undeformed theory.

Findings

Vacuum expectation values expressed as overlaps between MPS and Bethe states.

Deformation modifies the interpretation of the MPS as an integrable boundary state.

Numerical results support analytical findings for specific operators.

Abstract

We generalize earlier results on one-point functions in N = 4 SYM with a co-dimension one defect, dual to the D3-D5-brane setup in type IIB string theory on AdS5xS5, to a similar setup in the $\beta$-deformed version of the theory. The treelevel vacuum expectation values of single-trace operators in the two-scalar-subsector are expressed as overlaps between a matrix product state (MPS) and Bethe states in the corresponding twisted spin-chain picture. We comment on the properties of this MPS and present the simplest analytical overlaps and their behavior in a certain limit (of large k). Importantly, we note that the deformation alters earlier interpretations of the MPS as an integrable boundary state, seemingly obstructing simplifications of the overlaps analogous to the compact determinant formula found in the non-deformed theory. The results are supplemented with some supporting numerical results for operators of length eight with four excitations.