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240
The AdS5 × S 5 superstring worldsheet S-matrix and crossing symmetry
, 2008
"... An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in thi ..."
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Cited by 228 (6 self)
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An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS5 ×S 5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.
The su(2|2) dynamic S-matrix
, 2005
"... We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N = 4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain B ..."
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Cited by 222 (11 self)
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We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N = 4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equations for the su(2|3) dynamic spin chain and for N = 4 SYM.
Transcendentality and crossing
, 2006
"... We discuss possible phase factors for the S-matrix of planar N = 4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMNscaling, Kotikov-Lipatov transcendentality in the universal scaling function ..."
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Cited by 175 (2 self)
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We discuss possible phase factors for the S-matrix of planar N = 4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMNscaling, Kotikov-Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS5 × S 5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve
Magnon bound states and the AdS/CFT correspondence,” J.Phys
, 2006
"... We study the spectrum of asymptotic states in the spin-chain description of planar N = 4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation, ..."
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Cited by 155 (3 self)
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We study the spectrum of asymptotic states in the spin-chain description of planar N = 4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation,
Wrapping interactions and a new source of corrections to the spin-chain/string duality
, 2006
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The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
, 2006
"... We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the repr ..."
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Cited by 143 (6 self)
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We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction and investigation of an interesting S-matrix with su(2|2) symmetry. In particular, they enable a remarkably simple proof of the Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry’s R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with psu(2, 2|4) symmetry is sketched.
Quantum corrections to the string Bethe ansatz,” hep-th/0603204
"... hep–th/0603204 ..."
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Connecting giant magnons to the pp-wave: An interpolating limit
- of AdS5×S 5 ” [hep-th/0612079
"... We consider a particular large-radius limit of the worldsheet S-matrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the ..."
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Cited by 92 (0 self)
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We consider a particular large-radius limit of the worldsheet S-matrix for strings propagating on AdS5 × S 5. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The S matrix of the limiting theory is non-trivial, and receives contributions to all orders in the α ′ expansion. We analyze a guess for the full worldsheet S matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed S matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the S matrix
Wrapping interactions at strong coupling – the giant magnon
, 2008
"... We derive generalized Lüscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS5 × S⁵ superstring these formulas encode leading wrapping interaction effects. We apply the generalized µ-term formula to calculate finite size corrections to the dispersion ..."
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Cited by 90 (3 self)
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We derive generalized Lüscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS5 × S⁵ superstring these formulas encode leading wrapping interaction effects. We apply the generalized µ-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.
Long-range psu(2, 2|4) Bethe Ansätze for Gauge Theory and Strings
, 2005
"... We generalize various existing higher-loop Bethe ansätze for simple sectors of the integrable long-range dynamic spin chain describing planar N = 4 Super Yang-Mills Theory to the full psu(2, 2|4) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conject ..."
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Cited by 86 (5 self)
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We generalize various existing higher-loop Bethe ansätze for simple sectors of the integrable long-range dynamic spin chain describing planar N = 4 Super Yang-Mills Theory to the full psu(2, 2|4) symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct three-loop diagonalization and expected thermodynamic behavior. In the special case of the su(1|2) subsector, corresponding to a long-range t-J model, we are able to derive, up to three loops, the S-matrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel all-order S-matrices for the su(1|2) and psu(1, 1|2) subsectors, and show that they satisfy the Yang-Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS5 × S 5 is also described by a psu(2, 2|4) spin chain. We propose asymptotic all-order Bethe equations for this
