Article

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

Journal of High Energy Physics (Impact Factor: 5.62). 01/2011; 9. DOI:10.1007/JHEP09(2011)125

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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). · 5.62 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**The correspondence between the semiclassical limit of the DOZZ quantum Liouville theory and the Nekrasov-Shatashvili limit of the $ \mathcal{N} = 2 $ (Ω-deformed) U(2) super-Yang-Mills theories is used to calculate the unknown accessory parameter of the Fuchsian uniformization of the 4-punctured sphere. The computation is based on the saddle point method. This allows to find an analytic expression for the N f = 4, U(2) instanton twisted superpotential and, in turn, to sum up the 4-point classical block. It is well known that the critical value of the Liouville action functional is the generating function of the accessory parameters. This statement and the factorization property of the 4-point action allow to express the unknown accessory parameter as the derivative of the 4-point classical block with respect to the modular parameter of the 4-punctured sphere. It has been found that this accessory parameter is related to the sum of all rescaled column lengths of the so-called ’critical’ Young diagram extremizing the instanton ’free energy’. It is shown that the sum over the ’critical’ column lengths can be rewritten in terms of a contour integral in which the integrand is built out of certain special functions closely related to the ordinary Gamma function.Journal of High Energy Physics 01/2012; 2012(5). · 5.62 Impact Factor

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