The Resurgent Structure of Topological Strings

The Resurgent Structure of Topological Strings

Institut des Hautes Etudes Scientifiques (IHES) via YouTube Direct link

Intro

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1 of 7

Intro

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The Resurgent Structure of Topological Strings

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  1. 1 Intro
  2. 2 The search for a non-perturbative understanding of (topological) string theory has been going on for many years.
  3. 3 The resurgent structure associated to a formal power series is the set of all its alien derivatives at all its singularities (i.e. trans-series plus Stokes constants)
  4. 4 manifold M one can calculate periods by integrating the holomorphic 3-form over a symplectic basis of 3-cycles
  5. 5 String perturbation theory tells us that the total free energy is a formal power series involving a small parameter, a.k.a. the string coupling constant, and we have to sum over all genera
  6. 6 In this formulation, S is essentially an arbitrary variable. The conventional topological string free energies are recovered in the so-called holomorphic limit, where S becomes a (known) function of …
  7. 7 Experimental evidence: asymptotics in the quintic CY

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