The free field representation or "bosonization" rule1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and arbitrary central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, is quadratic in the fields. In this way, all known formulae for conformal blocks and correlators may be easily reproduced as certain linear combinations of correlators of these free fields. Generalization to conformal blocks on arbitrary Riemann surfaces is straightforward. However, projection rules in the spirit of Ref. 2 are not specified. The special role of βγ systems is emphasized. From the mathematical point of view, the construction involved represents generators of Kac-Moody (KM) algebra in terms of generators of a Heisenberg one. If WZW Lagrangian is considered as d−1 of Kirillov form on an orbit of KM algebra,3 then the free fields of interest (i.e. generators of the Heisenberg algebra) diagonalize Kirillov form and the action. Reduction of KM algebra within the same construction should naturally lead to arbitrary coset models.
The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger
equation in the equivariant integration over the moduli space of Higgs bundles
is revisited. We argue that the wave functions of the corresponding
two-dimensional topological U(N) gauge theory reproduce quantum wave functions
of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This
implies the full equivalence between the above gauge theory and the
$N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger
equation. This also implies the explicit correspondence between the gauge
theory and the representation theory of degenerate double affine Hecke algebra.
We propose similar construction based on the $G/G$ gauged WZW model leading to
the representation theory of the double affine Hecke algebra. The relation with
the Nahm transform and the geometric Langlands correspondence is briefly
discussed.Comment: 48 pages, typos corrected, one reference adde
A new class of infinite dimensional representations of the Yangians Y (g) and Y (b) corresponding to a complex semisimple algebra g and its Borel subalgebra b ⊂ g is constructed. It is based on the generalization of the Drinfeld realization of Y (g), g = gl(N ) in terms of quantum minors to the case of an arbitrary semisimple Lie algebra g. The Poisson geometry associated with the constructed representations is described. In particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of G-monopoles defined as the components of the space of based maps of P 1 into the generalized flag manifold X = G/B. Thus the constructed representations of the Yangian may be considered as a quantization of the moduli space of the monopoles.
We report Neutrino-4 experiment results of measurements of reactor antineutrinos flux and spectrum dependence on the distance in range 6-12 meters from the center of the reactor core. The fit of experimental dependence with the law 1 L 2 ⁄ , where L is the distance from the reactor center, gave satisfactory result with goodness of fit 81%. However, we discovered that the experimental neutrino spectrum is different from the calculated one. Using experimental spectrum, we performed the model independent analysis of restrictions on oscillation parameters ∆m 14 2 and sin 2 2 14 . The results of this analysis exclude area of reactor and gallium anomaly at CL more than 99.7% (> 3 ) for values ∆m 14 2 < 3eV 2 and sin 2 2θ 14 > 0.1 However, we observed an oscillation effect at CL 2.8 in vicinity of ∆m 14 2 ≈ 7.34eV 2 and sin 2 2θ 14 ≈ 0.39. The method of coherent addition of results of measurements, which allows us to directly observe the effect of oscillations, is proposed. The analysis of that effect is presented. In general, it seems that the effect predicted in gallium and reactor experiments is confirmed but at sufficiently large value of ∆m 14 2 . Future prospects of the experiment are discussed.
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