44,503 research outputs found

    The generalized multi-channel Kondo model: Thermodynamics and fusion equations

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    The SU(N) generalization of the multi-channel Kondo model with arbitrary rectangular impurity representations is considered by means of the Bethe Ansatz. The thermodynamics of the model is analyzed by introducing modified fusion equations for the impurity, leading to a simple description of the different IR fixed points of the theory. The entropy at zero temperature is discussed; in particular the overscreened case is explained in terms of quantum group representation.Comment: 41 pages, 8 figures, harvma

    Witten's Vertex Made Simple

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    The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte

    Monopole Operators in U(1)U(1) Chern-Simons-Matter Theories

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    We study monopole operators at the infrared fixed points of U(1)U(1) Chern-Simons-matter theories (QED3_3, scalar QED3_3, N=1{\cal N} =1 SQED3_3, and N=2{\cal N} = 2 SQED3_3) with NN matter flavors and Chern-Simons level kk. We work in the limit where both NN and kk are taken to be large with κ=k/N\kappa = k/N fixed. In this limit, we extract information about the low-lying spectrum of monopole operators from evaluating the S2×S1S^2 \times S^1 partition function in the sector where the S2S^2 is threaded by magnetic flux 4πq4 \pi q. At leading order in NN, we find a large number of monopole operators with equal scaling dimensions and a wide range of spins and flavor symmetry irreducible representations. In two simple cases, we deduce how the degeneracy in the scaling dimensions is broken by the 1/N1/N corrections. For QED3_3 at κ=0\kappa=0, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of NN. For N=2{\cal N} = 2 SQED3_3, we find that the lowest dimension monopole operator is generically non-BPS.Comment: 52 pages plus appendices, 9 figures, v2: minor correction
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