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      Integrability in QCD and beyond

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          Abstract

          Yang--Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang--Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang--Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a N=2 SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang--Mills dynamics with the hidden symmetry of a string theory on a curved background.

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          Hidden Symmetries of the AdS_5 x S^5 Superstring

          Attempts to solve Yang-Mills theory must eventually face the problem of analyzing the theory at intermediate values of the coupling constant. In this regime neither perturbation theory nor the gravity dual are adequate, and one must consider the full string theory in the appropriate background. We suggest that in some nontrivial cases the world sheet theory may be exactly solvable. For the Green-Schwarz superstring on AdS_5 x S^5 we find an infinite set of nonlocal classically conserved charges, of the type that exist in integrable field theories.
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            The Coulomb Phase of N=2 Supersymmetric QCD

            We present an explicit non-perturbative solution of N=2 supersymmetric SU(N_c) gauge theory with N_f \le 2N_c flavors generalizing results of Seiberg and Witten for N_c=2.
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              Exclusive Processes in Quantum Chromodynamics: The Form Factors of Baryons at Large Momentum Transfer

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                Author and article information

                Journal
                27 July 2004
                2004-09-02
                Article
                10.1142/S0217751X04019895
                hep-th/0407232
                e12e2aa4-6291-4ba0-a891-77e418e7b61e
                History
                Custom metadata
                Int.J.Mod.Phys.A19:4715-4788,2004
                87 pages, 4 figures; minor stylistic changes, references added. To be published in the memorial volume 'From Fields to Strings: Circumnavigating Theoretical Phyiscs', World Scientific, 2004. Dedicated to the memory of Ian Kogan
                hep-th hep-ph

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