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Register a new userBethe Equations on the Wrong Side of Equator
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G.P. Pronko
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We analyse the famous Baxters $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution which should corresponds to Bethe-Ansatz beyond $N/2$. This second solution of Baxters equation plays essential role and together with the first one gives rise to all fusion relations.
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Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization by zeta-function. Here we show that this matching is indeed correct up to fourth order in effective coupling; beyond, we find new contributions at odd powers. We show that these are reproduced by quantum corrections within the Bethe ansatz. They might also identify the three-loop discrepancy between string and gauge theory as an order-of-limits effect.
Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations on the wrong side of the equator (hep-th/9808153) is just zero (not only its action on the pseudovacuum).
We develop a framework for deriving Dyson-Schwinger Equations (DSEs) and Bethe-Salpeter Equation (BSE) in QCD at large $N_c$ limit. The starting point is a modified form (with auxiliary fields) of QCD generating functional. This framework provides a natural order-by-order truncation scheme for DSEs and BSE, and the kernels of the equations up to any order are explicitly given. Chiral symmetry (at chiral limit) is preserved in any order truncation, so it exemplifies the symmetry preserving truncation scheme. It provides a method to study DSEs and BSE beyond the Rainbow-Ladder truncation, and is especially useful to study contributions from non-Abelian dynamics (those arise from gluon self-interactions). We also derive the equation for the quark-ghost scattering kernel, and discuss the Slavnov-Taylor identity connecting the quark-gluon vertex, the quark propagator and the quark-ghost scattering kernel.
In [1, 2], Nekrasov applied the Bethe/gauge correspondence to derive the $mathfrak{su}, (2)$ XXX spin-chain coordinate Bethe wavefunction from the IR limit of a 2D $mathcal{N}=(2, 2)$ supersymmetric $A_1$ quiver gauge theory with an orbifold-type codimension-2 defect. Later, Bullimore, Kim and Lukowski implemented Nekrasovs construction at the level of the UV $A_1$ quiver gauge theory, recovered his result, and obtained further extensions of the Bethe/gauge correspondence [3]. In this work, we extend the construction of the defect to $A_M$ quiver gauge theories to obtain the $mathfrak{su} , ( M + 1 )$ XXX spin-chain nested coordinate Bethe wavefunctions. The extension to XXZ spin-chain is straightforward. Further, we apply a Higgsing procedure to obtain more general $A_M$ quivers and the corresponding wavefunctions, and interpret this procedure (and the Hanany-Witten moves that it involves) on the spin-chain side in terms of Izergin-Korepin-type specializations (and re-assignments) of the parameters of the coordinate Bethe wavefunctions.
In contrast to other fields where conferences are typically for less polished or in-progress research, computing has long relied on referred conference papers as a venue for the final publication of completed research. While frequently a topic of informal discussion, debates about its efficacy, or library science research, the development of this phenomena has not been historically analyzed. This paper presents the first systematic investigation of the development of modern computing publications. It relies on semi-structured interviews with eight computing professors from diverse backgrounds to understand how researchers experienced changes in publication culture over time. Ultimately, the article concludes that the early presence of non-academic practitioners in research and a degree of path dependenceor a tendency to continue on the established path rather than the most economically optimal one allowed conferences to gain and hold prominence as the field exploded in popularity during the 1980s.
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