Abstract
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 SU( N) κ Verlinde ring turns out to lead to affine Toda equations of SU( N) type satisfied by the ground state metric.
Highlights
N = 2 supersymmetric quantum field theories have recently undergone an intensive investigation from many different points of view: From the string point of view N = 2 superconformal models in 2 dimensions constitute the building blocks of N = 1 space-time supersymmetric string vacua [1]
In particular many of our N = 2 massive supersymmetric theories are themselves described by quantum affine Toda theories. In these cases we find that the ground state metric, which could be viewed as some particular correlation functions in these theories, as a function of the overall coupling satisfy ordinary classical affine Toda equations of the same type
In addition to the models that can be reduced to Today systems there are those for which the ground state metric decomposes in two “non-interacting” sectors one of which can be recast in a Toda form
Summary
In particular we can move it to the boundary of the hemisphere, in which case by operator formulation we see that the state is the same as multiplication of the state by the field ~, H) =~I0), agreeing with the previous definition Note that in this equation by I i) we mean the topological class of the state, i.e. I i) may differ from an actual ground state of the theory by Q k-closed states. From the above path-integral definition it follows that essentially both metrics are topological, where by topological we mean if we perturb the corresponding positions of inserted fields or the metric on the hemisphere, as long as there is an infinitely long intermediate cylinder, with a fixed perimeter 13, the result of the path-integral does not change This is due to the fact that local perturbations of this kind, as noted above, are equivalent to operations by Q~or on some state, and propagation along the cylinder of length T results in exp(—TH)Q~.
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