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Open accessJournal ArticleDOI
Neil R. Constable, Finn Larsen 
77 Citations
The matrix integrals arising here also determine the correlation functions of gauge invariant operators in two dimensional Yang-Mills theory, suggesting an equivalence between the rolling tachyon and QCD2.
We show that q-integration of the Stieltjes–Wigert matrix model is the discrete matrix model that describes q-deformed Yang–Mills theory on S2.
The classical part of the $R$-matrix itself satisfies the quantum Yang-Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part.
We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.
Along a specific line our maximal coupling agrees with that of a new exact S-matrix that corresponds to an elliptic deformation of the supersymmetric Sine-Gordon model which preserves unitarity and solves the Yang-Baxter equation.
In case the invariance with respect to the centrally extended algebra is not sufficient to fully specify the scattering matrix, the requirement of Yangian symmetry provides an alternative to the Yang-Baxter equation and leads to a complete, up to an overall phase, determination of the S-matrix.
We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer.
We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix.
We show that the fundamental R-matrix of the model (which satisfies a difference property Yang-Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part.

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