Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-07-25
JHEP 0612:070,2006
Physics
High Energy Physics
High Energy Physics - Theory
50 pages; v2: small typos fixed, references added; v3: cosmetic changes, published version; v4: typos fixed, small clarificati
Scientific paper
10.1088/1126-6708/2006/12/070
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 $\IP{\Psi | g | \Omega}$ of the Schr\"odinger-Weil representation of a Heisenberg extension of $G$, between an arbitrary state $\bra{\Psi}$ and a particular vacuum state $\ket{\Omega}$. 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.
Gunaydin Murat
Neitzke Andrew
Pioline Boris
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