Superconformal coset equivalence from level-rank duality

Abstract

We construct a one-to-one map between the primary fields of the N = 2 superconformal Kazama-Suzuki models G(m, n, k) and G(k, n, m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(1) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.

Large-N limits of 2d CFTs, quivers and AdS3 duals

“…level-rank duality [6]. This particular duality bears similarities with the Seiberglike duality of the one-adjoint A n+1 CSM theories in three dimensions [7,8] and the Seiberg-Kutasov duality of corresponding one-adjoint SQCD theories in four dimensions [9].…”

“…coset by level-rank duality, [6]. In this dual version of the CFT one starts from an SU(N )× SU(N ) flavor symmetry and then gauges the diagonal subgroup.…”

“…To find the large-N limits we must analyze the scaling of the quadratic Casimir for SU(N ) representations, with the result 6) in the N → ∞ limit for representations with an O(1) number of boxes in their Young tableau. We can give a general formula for the quadratic Casimir C 2 (R) = C 2 (R), corresponding to a Young tableau with m 1 boxes in the first column, m 2 boxes in the second column etc, with the m i ordered, m 1 ≥ m 2 ≥ m 3 · · · .…”

Higher spin AdS3 holography with extended supersymmetry

“…The label ΛN for su(N )N+M should be related to the label ΛN+M in (3.5) for su(N + M )N by the action of transpose as usual for the level-rank duality, see, e.g., [52].…”

Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories

“…where the left and right models are equivalent by the level-rank duality [12,13,27,28]. The central charge of this Kazama-Suzuki model is c = 3nk k+n+1 .…”