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Topological–anti-topological fusion. (English) Zbl 1136.81403

Summary: We study some non-perturbative aspects of \(N=2\) supersymmetric quantum field theories (both superconformal and massive deformations thereof). We show that the metric for the supersymmetric ground states, which in the conformal limit is essentially the same as Zamolodchikov’s metric, is pseudo-topological and can be viewed as a result of fusion of the topological version of \(N=2\) theory with its conjugate. For special marginal/relevant deformations (corresponding to theories with factorizable \(S\)-matrix), the ground state metric satisfies classical Toda/Affine Toda equations as a function of perturbation parameters. The unique consistent boundary conditions for these differential equations seem to predict the normalized OPE of chiral fields at the conformal point. Also the subset of \(N=2\) theories whose chiral ring is isomorphic to \(\mathrm{SU}(N)_{\kappa}\) Verlinde ring turns out to lead to affine Toda equations of \(\mathrm{SU}(N)\) type satisfied by the ground state metric.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
58Z05 Applications of global analysis to the sciences
81T60 Supersymmetric field theories in quantum mechanics
81T70 Quantization in field theory; cohomological methods
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