A solvable tensor field theory

  • Romain PascalieEmail author


We solve the closed Schwinger–Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert’s W function, using a perturbative expansion and Lagrange–Bürmann resummation. Higher-point functions are then obtained recursively.


Schwinger–Dyson equation Series expansion and resummation Tensor field theory 

Mathematics Subject Classification

35Q99 81T99 30B40 40E99 



The author would like to thank Raimar Wulkenhaar for his guidance throughout this project, Adrian Tanasa for his advice and comments on the manuscript and Alexander Hock for helpful discussions.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.LaBRIUniversité de BordeauxTalenceFrance
  2. 2.Mathematisches Institut der Westfälischen Wilhelms-UniversitätMünsterGermany

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