Abstract:
We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also partially break the supersymmetry. In spite of the regularization, one can establish a homotopy of the elliptic genus in a coupling parameter. Our construction relies on a priori estimates and other methods from constructive quantum field theory; this mathematical underpinning allows us to justify evaluating the elliptic genus at one endpoint of the homotopy. We obtain a version of Witten's proposed formula for the elliptic genus in terms of classical theta functions. As a consequence, the elliptic genus has a hidden SL(2, ℤ) symmetry characteristic of conformal theory, even though the underlying theory is not conformal.
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Received: 7 January 2000 / Accepted: 10 April 2000
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Jaffe, A. The Elliptic Genus and Hidden Symmetry. Commun. Math. Phys. 219, 89–124 (2001). https://doi.org/10.1007/PL00005564
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DOI: https://doi.org/10.1007/PL00005564