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23
Threepoint function of semiclassical states at weak coupling
, 2012
"... We give the derivation of the previously announced analytic expression for the correlation function of three heavy nonBPS operators in N = 4 superYangMills theory at weak coupling. The three operators belong to three different su(2) sectors and are dual to three classical strings moving on the sp ..."
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Cited by 24 (5 self)
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We give the derivation of the previously announced analytic expression for the correlation function of three heavy nonBPS operators in N = 4 superYangMills theory at weak coupling. The three operators belong to three different su(2) sectors and are dual to three classical strings moving on the sphere. Our computation is based on the reformulation of the problem in terms of the Bethe Ansatz for periodic XXX spin1/2 chains. In these terms the three operators are described by longwavelength excitations over the ferromagnetic vacuum, for which the number of the overturned spins is a finite fraction of the length of the chain, and the classical limit is known as the Sutherland limit. Technically our main result is a factorized operator expression for the scalar product of two Bethe states. The derivation is based on a fermionic representation of Slavnov’s determinant formula, and a subsequent bosonisation.
Wave functions and correlation functions for GKP strings from integrability
, 2012
"... We develop a general method of computing the contribution of the vertex operators to the semiclassical correlation functions of heavy string states, based on the stateoperator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of ..."
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Cited by 18 (2 self)
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We develop a general method of computing the contribution of the vertex operators to the semiclassical correlation functions of heavy string states, based on the stateoperator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the threepoint functions of the large spin limit of the GubserKlebanovPolyakov (GKP) strings in AdS3 spacetime, left unevaluated in our previous work [arXiv:1110.3949] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite threepoint functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.
Partial domain wall partition functions
 JHEP 1207 (2012) 186, [arXiv:1205.4400 [mathph
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Inner products of Bethe states as partial domain wall partition functions
, 2012
"... We study the inner product of Bethe states in the inhomogeneous periodic XXX spin1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an onshellMmagnon state with a generic Mmagnon state is given by the same expression as the inner product o ..."
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Cited by 15 (4 self)
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We study the inner product of Bethe states in the inhomogeneous periodic XXX spin1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an onshellMmagnon state with a generic Mmagnon state is given by the same expression as the inner product of a 2Mmagnon state with a vacuum descendent. The second inner product is proportional to the partition function of the sixvertex model on a rectangular L × 2M grid, with partial domainwall boundary conditions.
Slavnov determinants, YangMills structure constants, and discrete KP,” ArXiv eprints
, 2012
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Novel construction and the monodromy relation for threepoint fuctions at weak coupling
"... In this article, we shall develop and formulate two novel viewpoints and properties concerning the threepoint functions at weak coupling in the SU(2) sector of the N = 4 super YangMills theory. One is a double spinchain formulation of the spinchain and the associated new interpretation of the o ..."
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Cited by 1 (0 self)
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In this article, we shall develop and formulate two novel viewpoints and properties concerning the threepoint functions at weak coupling in the SU(2) sector of the N = 4 super YangMills theory. One is a double spinchain formulation of the spinchain and the associated new interpretation of the operation of Wick contraction. It will be regarded as a skew symmetric pairing which acts as a projection onto a singlet in the entire SO(4) sector, instead of an inner product in the spinchain Hilbert space. This formalism allows us to study a class of threepoint functions of operators built upon more general spinchain vacua than the special configuration discussed so far in the literature. Furthermore, this new viewpoint has the significant advantage over the conventional method: In the usual “tailoring ” operation, the Wick contraction produces inner products between offshell Bethe states, which cannot be in general converted into simple expressions. In contrast, our procedure directly produces the socalled partial domain wall partition functions, which can be expressed as determinants. Using this property, we derive simple determinantal representation for a broader class of threepoint functions. The second new property uncovered in this work is the nontrivial identity satisfied by the threepoint functions with monodromy operators inserted. Generically this relation connects threepoint functions of different operators and can be regarded as a kind of SchwingerDyson equation. In particular, this identity reduces in the semiclassical limit to the triviality of the product of local monodromies Ω1Ω2Ω3 = 1 around the vertex operators, which played a crucial role in providing all important global information on the threepoint function in the strong coupling regime [arXiv:1312.3727]. This structure may provide a key to the understanding of the notion of “integrability ” beyond the spectral level.