2019/09/30 by Miroslav Rapčák, Miroslav Rapcak
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Calabi–Yau manifold #Gravitational singularity #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep01(2020)042
published as JHEP01(2020)042 · 39 pages
arxiv created 2019/09/30 · openalex created_date 2019/10/10 · openalex publication_date 2020/01/08 · arxiv updated 2020/01/15 · openalex updated_date 2026/08/05
A bstract We discuss a class of vertex operator algebras W.m|n\kern0.33em × \kern0.33em ∞ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mrow> <mml:mfenced> <mml:mi>m</mml:mi> </mml:mfenced> <mml:mi>n</mml:mi> <mml:mspace/> <mml:mo>×</mml:mo> <mml:mspace/> <mml:mo>∞</mml:mo> </mml:mrow> </mml:msub> </mml:math> generated by a super- matrix of fields for each integral spin 1 , 2 , 3 , . . . . The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to xy = z m w n . We propose a free-field realization of such truncations generalizing the Miura transformation for WN <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> algebras. Relations in the ring of holomorphic functions lead to bosonization-like relations between different free-field realizations. The discussion provides a concrete example of a non-trivial interplay between vertex operator algebras, algebraic geometry and gauge theory.