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Motives of melonic graphs

Aluffi, Paolo and Marcolli, Matilde and Qaisar, Waleed (2020) Motives of melonic graphs. . (Unpublished)

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We investigate recursive relations for the Grothendieck classes of the affine graph hypersurface complements of melonic graphs. We compute these classes explicitly for several families of melonic graphs, focusing on the case of graphs with valence-4 internal vertices, relevant to CTKT tensor models. The results hint at a complex and interesting structure, in terms of divisibility relations or nontrivial relations between classes of graphs in different families. Using the recursive relations we prove that the Grothendieck classes of all melonic graphs are positive as polynomials in the class of the moduli space M_(0,4). We also conjecture that the corresponding polynomials are log-concave, on the basis of hundreds of explicit computations.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:The first author acknowledges support from a Simons Foundation Collaboration Grant, award number 625561, and thanks the University of Toronto for hospitality. The second author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics. The third author worked on parts of this project as summer undergraduate research at the University of Toronto.
Funding AgencyGrant Number
Simons Foundation625561
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Record Number:CaltechAUTHORS:20210825-184604511
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110546
Deposited By: George Porter
Deposited On:25 Aug 2021 22:15
Last Modified:25 Aug 2021 22:15

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