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Journal of High Energy Physics

, 2018:114 | Cite as

One-point functions in β-deformed \( \mathcal{N}=4 \) SYM with defect

  • Erik WidénEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We generalize earlier results on one-point functions in \( \mathcal{N}=4 \) SYM with a codimension one defect, dual to the D3-D5-brane setup in type IIB string theory on AdS5 ×S5, to a similar setup in the β-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.

Keywords

AdS-CFT Correspondence Duality in Gauge Field Theories Integrable Field Theories Lattice Integrable Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.NORDITA, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden
  2. 2.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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