Topological wave functions and heat equations

Murat Günaydin, Andrew Neitzke, Boris Pioline

Research output: Contribution to journalReview articlepeer-review

35 Scopus citations


It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise: (i) we give a new, purely holomorphic version of the holomorphic anomaly equations, clarifying their relation to the heat equation satisfied by the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian symmetric tube domain G/K, we show that the general solution of the anomaly equations is a matrix element 〈;Ψ|g|Ω〉 of the Schrödinger-Weil representation of a Heisenberg extension of G, between an arbitrary state 〈Ψ| and a particular vacuum state |Ω〉. Based on these results, we speculate on the existence of a one-parameter generalization of the usual topological amplitude, which in symmetric cases transforms in the smallest unitary representation of the duality group G′ in three dimensions, and on its relations to hypermultiplet couplings, nonabelian Donaldson-Thomas theory and black hole degeneracies.

Original languageEnglish (US)
Article number070
JournalJournal of High Energy Physics
Issue number12
StatePublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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