Prepared for submission to JHEP Moduli Stabilisation and the Holographic Swampland Joseph P. Conlon,a Filippo Revelloa aRudolf Peierls Centre for Theoretical Physics Beecroft Building, Clarendon Laboratory, Parks Road, University of Oxford, OX1 3PU, UK E-mail:
[email protected],
[email protected] 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 ∆ϕ = 8.038) also appears to live very close to a critical value (∆ϕ = 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. arXiv:2006.01021v2 [hep-th] 28 Aug 2020 Contents 1 Introduction2 2 The Large Volume Scenario and its Holographic Properties4 2.1 Introduction to LVS and its low energy dynamics4 2.2 CFT interpretation6 2.3 Connection to the Swampland6 3 Holographic CFTs and Consistency Conditions8 3.1 Holographic CFTs8 3.2 The Bootstrap9