# Non-commutative $AdS_2/CFT_1$ duality: the case of massive and interacting scalar fields

## TL;DR

This paper investigates the non-commutative $AdS_2/CFT_1$ duality, extending previous work to include massive and interacting scalar fields, and confirms non-commutative corrections preserve certain correlation function forms.

## Contribution

It extends the non-commutative $AdS_2/CFT_1$ analysis to massive and interacting scalars, showing non-trivial conformal behavior without a direct map to the commutative case.

## Key findings

- Leading order non-commutative corrections preserve 2- and 3-point correlator forms.
- No map exists connecting commutative and non-commutative models.
- Non-commutative correlators exhibit conformal behavior as in the dual CFT.

## Abstract

We continue the study of the nocommutative $AdS_2 / CFT_1$ correspondence. We extend our previous results obtained for a free massless scalar field to the case of a massive scalar field. Both the free and interacting cases are considered. For both cases it is confirmed that to the leading order in noncommutative corrections the 2- and 3-point correlation functions have the form that is assumed by some (yet unspecified) dual $CFT$. We also argue that there does not exist a map which connects the commutative model to its non-commutative counterpart, and therefore the conformal behaviour of the noncommutative correlators is a non-trivial result.