Counting Large Maps

  • Bertrand Eynard
Part of the Progress in Mathematical Physics book series (PMP, volume 70)


Initially, in quantum gravity and string theory, the problem of counting maps, i.e. surfaces made of polygons, was introduced only as a discretized approximation for counting continuous surfaces. The physical motivation is the following: in string theory, particles are 1-dimensional loops called strings, and under time evolution their trajectories in space-time are surfaces. Quantum mechanics amounts to averaging over all possible trajectories between given initial and final states, i.e. all possible surfaces between given boundaries. However, trajectories should be counted only once modulo their symmetries, in particular conformal reparametrizations, in other words, trajectories are in fact Riemann surfaces (equivalence class of surfaces modulo conformal reparametrizations).


Minimal Model Spectral Curve Conformal Field Theory String Equation Pure Gravity 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Bertrand Eynard
    • 1
  1. 1.CEA Saclay Institut de Physique Théorique (IPHT)Gif sur YvetteFrance

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