Open Access
January 2011 Two-dimensional topological field theories as taffy
Matt Ando, Eric Sharpe
Adv. Theor. Math. Phys. 15(1): 179-244 (January 2011).


In this paper, we use trivial defects to define global taffy-like operations on string worldsheets, which preserve the field theory. We fold open and closed strings on a space $X$ into open strings on products of multiple copies of $X$, and perform checks that the “taffy-folded” worldsheets have the same massless spectra and other properties as the original worldsheets. Such folding tricks are a standard method in the defects community; the novelty of this paper lies in deriving mathematical identities to check that e.g., massless spectra are invariant in topological field theories. We discuss the case of the B model extensively, and also derive the same identities for string topology, where they become statements of homotopy invariance. We outline analogous results in the A model, B-twisted Landau–Ginzburg models, and physical strings. We also discuss the understanding of the closed string states as the Hochschild homology of the open string algebra, and outline possible applications to elliptic genera.


Download Citation

Matt Ando. Eric Sharpe. "Two-dimensional topological field theories as taffy." Adv. Theor. Math. Phys. 15 (1) 179 - 244, January 2011.


Published: January 2011
First available in Project Euclid: 24 April 2012

zbMATH: 1246.81334
MathSciNet: MR2888011

Rights: Copyright © 2011 International Press of Boston

Vol.15 • No. 1 • January 2011
Back to Top