Moduli Stabilisation and the Holographic Swampland

TL;DR

This paper explores how Swampland constraints on string vacua in AdS relate to CFT data, revealing a negativity condition on anomalous dimensions that parallels causality bounds and connecting to the Swampland Distance Conjecture.

Contribution

It establishes a link between Swampland constraints and CFT anomalous dimensions, providing a new perspective on consistency conditions for string vacua and their holographic duals.

Findings

Swampland constraints correspond to negativity conditions on mixed anomalous dimensions.

LVS vacuum is near a critical anomalous dimension value where sign changes occur.

Connections are drawn between Swampland conditions and the Swampland Distance Conjecture.

Abstract

We investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, and both perturbative and racetrack stabilisation. Interestingly, the LVS vacuum (with $\Delta_{\varphi} = 8.038$) also appears to live very close to a critical value ($\Delta_{\varphi} = 8$) where the anomalous dimensions change sign. We finally point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions.