2008/07/31 by A. Mironov, A Mironov, A. Morozov +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Geometry and complex manifolds #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.AG #math.MP
paper · pdf · doi:10.1088/1126-6708/2009/02/024
published as JHEP 0902:024,2009 · 36 pages
arxiv created 2008/09/14 · openalex publication_date 2009/02/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
M.Kazarian and S.Lando found a 1-parametric interpolation between Kontsevich and Hurwitz partition functions, which entirely lies within the space of KP tau-functions. V.Bouchard and M.Marino suggested that this interpolation satisfies some deformed Virasoro constraints. However, they described the constraints in a somewhat sophisticated form of AMM-Eynard equations for the rather involved Lambert spectral curve. Here we present the relevant family of Virasoro constraints explicitly. They differ from the conventional continuous Virasoro constraints in the simplest possible way: by a constant shift u2/24 of the L-1 operator, where u is an interpolation parameter between Kontsevich and Hurwitz models. This trivial modification of the string equation gives rise to the entire deformation which is a conjugation of the Virasoro constraints Lm -> U Lm U-1 and "twists" the partition function, ZKH= U ZK. The conjugation U is expressed through the previously unnoticed operators which annihilate the quasiclassical (planar) free energy of the Kontsevich model, but do not belong to the symmetry group GL(∞) of the universal Grassmannian.