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Baxter’s Qoperators for supersymmetric spin chains
"... We develop YangBaxter integrability structures connected with the quantum affine superalgebra Uq ( sl(21)). Baxter’s Qoperators are explicitly constructed as supertraces of certain monodromy matrices associated with (qdeformed) bosonic and fermionic oscillator algebras. There are six different ..."
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Cited by 31 (3 self)
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We develop YangBaxter integrability structures connected with the quantum affine superalgebra Uq ( sl(21)). Baxter’s Qoperators are explicitly constructed as supertraces of certain monodromy matrices associated with (qdeformed) bosonic and fermionic oscillator algebras. There are six different Qoperators in this case, obeying a few fundamental fusion relations, which imply all functional relations between various commuting transfer matrices. The results are universal in the sense that they do not depend on the quantum space of states and apply both to lattice models and to continuous quantum field theory models as well. 1
Solutions of the Tsystem and Baxter equations for supersymmetric spin chains”, arXiv:0906.2039
"... We propose Wronskianlike determinant formulae for the Baxter Qfunctions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra Uq ( ̂ gl(MN)). In contrast to the supersymmetric BazhanovReshetikhin formula (the quantum supersymmetric JacobiTrudi form ..."
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Cited by 18 (4 self)
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We propose Wronskianlike determinant formulae for the Baxter Qfunctions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra Uq ( ̂ gl(MN)). In contrast to the supersymmetric BazhanovReshetikhin formula (the quantum supersymmetric JacobiTrudi formula) proposed in [Z. Tsuboi, J. Phys. A: Math. Gen. 30 (1997) 7975], the size of the matrices of these Wronskianlike formulae is less than or equal to M + N. Base on these formulae, we give new expressions of the solutions of the Tsystem (fusion relations for transfer matrices) for supersymmetric spin chains proposed in the abovementioned paper. Baxter equations also follow from the Wronskianlike formulae. They are finite order linear difference equations with respect to the Baxter Qfunctions. Moreover, the Wronskianlike formulae also explicitly solve the functional relations for Bäcklund flows proposed in [V. Kazakov, A. Sorin,
Z.Tsuboi, Baxter’s Qoperators and operatorial Bäcklund flow for quantum (super)spin chains
 Commun. Math. Phys
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Fusion hierarchies for N = 4 superYangMills theory, arXiv:0803.2035 [hepth
"... We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finitedimensional atypical representations in the auxiliary space for the putative longrange spin chain encoding anomalous dimensions of all composite singletrace gauge invariant operators of the maximally supe ..."
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Cited by 7 (1 self)
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We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finitedimensional atypical representations in the auxiliary space for the putative longrange spin chain encoding anomalous dimensions of all composite singletrace gauge invariant operators of the maximally supersymmetric YangMills theory. They obey an infinite fusion hierarchy which can be reduced to a finite set of integral relations for a minimal set of transfer matrices. This set is used to derive a finite systems of functional equations for eigenvalues of nested Baxter polynomials. 1
Firstprinciples derivation of the AdS/CFT Ysystems
 Journal of High Energy Physics
, 2011
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The Master TOperator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2014
"... we show how to construct the master Toperator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspon ..."
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Cited by 1 (1 self)
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we show how to construct the master Toperator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master Toperator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars–Schneider system of particles.
arXiv:1104.2474v2 [hepth] 6 Jul 2011
"... Abstract. This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians ..."
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Abstract. This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected in a fiveyear span of research on the subject. We hope this exercise will be useful for future attempts to study Yangians in field and string theories, with or without supersymmetry 1 .