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

(Impact Factor: 6.11). 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 $$\mathcal{N} = 2$$ 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
= 2N
c
flavors the other turns out to be $${\text{SU}}{(2)^{{N_c} - 3}}$$ with N
c
hyper-multiplets (N
c
> 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.

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• "The supersymmetric vacua of the N = 2 theory are in one-to-one correspondence with the eigenstates of the quantum integrable system labeled by – 1 – the solutions of the Bethe ansatz. The so-called Bethe/Gauge correspondence has given us new insights into dualities and symmetries between gauge theories [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]. 1 For example, it has been used to establish new 2d/4d dualities [23] [24] and 3d/5d dualities [25] [26] [27], to shed light on two-dimensional Seiberg-like dualities [28] [29], and three-dimensional mirror symmetry [30]. The correspondence also solves quantum integrable models in finite volume, as it gives rise to thermodynamic Bethe ansatz equations by summing the instantons [6, 31–34]. "
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