Remarks on Associated Varieties and Minimal Tension Holography

2025/07/17 by Ferrari, Andrea E. V.
Engineering · #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2507.13223

Abstract

We comment on certain analogies that have recently emerged between path integral localisation phenomena in minimal tension string theory on AdS₃× S³× T⁴ and associated varieties of boundary vertex algebras of 3d N=4 theories. We give evidence for the fact that the path integral localisation relies on an intriguing relation between the conformal boundary of AdS₃ and the associated variety of V₁(\mathfrakpsl(2|2)), (the complexification of) the affine algebra that enters the world-sheet description of the string theory. We explain the origin of certain operators (related to ``secret representations") that have appeared in this description. Based on the expectation that similar statements will hold for AdS₅× S⁵, we explicitly write down free field realisations of V₁(\mathfrakpsl(4|4)) that may hopefully be useful to study the world-sheet dual of free N=4 SYM.

Citations

• String theory in twistor space and minimal tension holography
• Solving AdS₃ string theory at minimal tension: tree-level correlators
• Celestial holography and AdS3/CFT2 from a scaling reduction of twistor space
• Free field realisation of boundary vertex algebras for Abelian gauge theories in three dimensions
• Classical freeness of orthosymplectic affine vertex superalgebras
• Vertex algebras associated with hypertoric varieties
• Gerbes of chiral differential operators

Related

• Solving AdS₃ string theory at minimal tension: tree-level correlators
• String theory in twistor space and minimal tension holography
• A note on background independence in AdS₃ string theory
• Topological defects and tensionless holography
• Spectral flow and localisation in AdS₃ string theory