Averaging over moduli in deformed WZW models. (English) Zbl 1472.81206
Summary: WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have \(N\) abelian conserved currents and central charge \(c > N \). We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as \( \mathrm{U}(1)^{2N}\) Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.
MSC:
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 83E05 | Geometrodynamics and the holographic principle |
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