Scheme dependence and instability of double-trace deformations for gauge fields in AdS$_5$

TL;DR

This paper examines how double-trace deformations in AdS$_5$ holography can lead to instabilities and scheme dependence when introducing dynamical gauge fields, highlighting the limitations of this approach due to tachyonic and ghost modes.

Contribution

It reveals the scheme dependence and instability issues in using double-trace deformations for gauge fields in AdS$_5$, supported by analytical and numerical analyses.

Findings

Identification of tachyon and ghost modes caused by scheme dependence.

Logarithmic behavior near the AdS boundary leads to instabilities.

Instabilities are demonstrated in both bottom-up and top-down models.

Abstract

In holography, double-trace deformations provide a general framework for deforming boundary field theories. In particular, they can be utilized to introduce dynamical gauge fields in the boundary theory through double-trace deformations of bulk gauge fields. In this work, we study this construction in the case where the bulk geometry is asymptotically AdS$_5$, and find that such a system involves tachyon and ghost modes. This instability originates from the logarithmic behavior of the gauge fields in the vicinity of the AdS boundary, which leads to a scheme-dependent ambiguity in the double-trace deformation. We investigate this instability by using both analytical and numerical methods in several holographic setups, including bottom-up models and the top-down D3-D7 construction.