Abstract
We study the two-point function of the stress-tensor multiplet of mathcal{N} = 4 SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the 20′ irrep of the mathfrak{so} (6)R R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial. We use a combination of perturbation theory and defect CFT techniques to obtain results up to next-to-leading order in the coupling constant. Being a defect CFT correlator, there exist two (super)conformal block expansions which capture defect and bulk data respectively. We present a closed-form formula for the defect CFT data, which allows to write an efficient Taylor series for the correlator in the limit when one of the operators is close to the line. The bulk channel is technically harder and closed-form formulae are particularly challenging to obtain, nevertheless we use our analysis to check against well-known data of mathcal{N} = 4 SYM. In particular, we recover the correct anomalous dimensions of a famous tower of twist-two operators (which includes the Konishi multiplet), and successfully compare the one-point function of the stress-tensor multiplet with results obtained using matrix-model techniques.
Highlights
The maximally extended supersymmetric Yang-Mills theory in four dimensional space-time (N = 4 SYM) [1] is a prime theoretical laboratory in quantum field theory
We focus on the single-trace operator of conformal dimension two that sits in the 20 irrep of the so(6)R R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial
The same can be said about correlators of 1/2-BPS operators, which have been a great source of non-trivial checks of the correspondence
Summary
In this work we will not use the bootstrap approach but rather perform an explicit perturbative computation up to next-to-leading order (NLO) As it will be clear in the main text, the use of modern defect CFT results will be crucial for our success, in particular, correlators of 1/2-BPS operators are severely constrained by Ward identities which were carefully studied in [41]. These powerful constraints together with a novel combination of perturbation theory, defect CFT techniques and numerical integration will allow us to obtain an exact formula for the defect channel data, which is basically a solution of the problem and can be used to produce an efficient Taylor series around the defect OPE limit (z, z) ∼ 0.
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