Baxter’sT-Q equation, SU(N)/SU(2) N − 3 correspondence and Ω-deformed Seiberg-Witten prepotential

Journal of High Energy Physics (Impact Factor: 6.22). 09/2011; 9(9). DOI: 10.1007/JHEP09(2011)125

ABSTRACT We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU( N)/SU(2) N-3 correspondence is found. That is, two kinds of 4D {N} = 2 superconformal field theories having the above different gauge groups are encoded simultaneously in one Baxter's T-Q equation which captures their spectral curves. For example, while one is SU( N c ) with N f = 2 N c flavors the other turns out to be {{SU}}{(2)^{{N_c} - 3}} with N c hyper-multiplets ( N c > 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.

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    • "(8vertex) ± (z, q, n) = θ 2n+1 1 (z|q) θ n 1 (3z|q 3 ) Q ± (z, q, n) satisfy the non-stationary Lamé equation: 6q ∂ ∂q Ψ (8vertex) ± (z, q, n) = 1 π 2 − ∂ 2 ∂z 2 + 9n(n + 1)℘(3z|q 3 ) + c(q, n) Ψ (8vertex) ± (z, q, n). (2.2) 2 See [18] [19] [20] [21] [22] "
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    ABSTRACT: We study the link between WZW model and the spin-1/2 XYZ chain. This is achieved by comparing the second-order differential equations from them. In the former case, the equation is the Ward-Takahashi identity satisfied by one-point toric conformal blocks. In the latter case, it arises from Baxter's TQ relation. We find that the dimension of the representation space w.r.t. the V-valued primary field in these conformal blocks gets mapped to the total number of chain sites. By doing so, Stroganov's "The Importance of being Odd" (cond-mat/0012035) can be consistently understood in terms of WZW model language. We first confirm this correspondence by taking a trigonometric limit of the XYZ chain. That eigenstates of the resultant two-body Sutherland model from Baxter's TQ relation can be obtained by deforming toric conformal blocks supports our proposal.
    Journal of High Energy Physics 02/2012; 2012(6). DOI:10.1007/JHEP06(2012)121 · 6.22 Impact Factor
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    ABSTRACT: In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.
    Journal of High Energy Physics 12/2011; 2012(4). DOI:10.1007/JHEP04(2012)105 · 6.22 Impact Factor
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    ABSTRACT: We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality.
    JETP Letters 04/2012; 97(1). DOI:10.1134/S0021364013010062 · 1.36 Impact Factor
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