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## Wrapping in maximally supersymmetric and marginally deformed N=4

Venue: | Yang-Mills |

Citations: | 19 - 0 self |

### Citations

5606 | The large N limit of superconformal field theories and supergravity
- Maldacena
- 1998
(Show Context)
Citation Context ...integrability, much progress has been made towards confirming the complete identification of the planar spectra of N = 4 gauge theory and AdS5 × S5 string theory implied by the AdS/CFT correspondence =-=[1]-=-. First, the construction of the scattering matrix and the asymptotic Bethe ansatz [2, 3] turned reachable the spectrum of asymptotically long operators and infinitely fast strings in the supergravity... |

311 |
The dilatation operator of
- Beisert, Kristjansen, et al.
- 2003
(Show Context)
Citation Context ...her. Let us now exhibit the symmetry between both values of β at the level of the spin chain Hamiltonian. The undeformed Hamiltonian can be written as a linear combination of generalized permutations =-=[21]-=-, ∑L−1 {a1, . . ., an} ≡ l=0 Pa1+l, a1+l+1 · · ·Pan+l, an+l+1 , (2.4) where the Pi, i+1 permutes the spins at sites i and i + 1 and can be written in terms of the Pauli matrices as Pi, i+1 = 1 ( 1i, i... |

153 | Wrapping interactions and a new source of corrections to the spin-chain / string duality, Nucl. Phys. B736
- Ambjorn, Janik, et al.
- 2006
(Show Context)
Citation Context ...n the perturbative order reaches the length L of the gauge invariant operator [5] while in the string theory finite-size effects come from virtual corrections traveling around the worldsheet cylinder =-=[6]-=-. Recently, however, even wrapping effects have started to become manageable. The four-loop anomalous dimension of the Konishi operator, which is the simplest case where wrapping effects are present, ... |

122 |
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B807
- Bajnok, Janik
- 2009
(Show Context)
Citation Context ...resent, has been obtained both from perturbative computations on the gauge theory side [7] and from a thermodynamic Bethe ansatz calculation based on the quantum field theory of the string worldsheet =-=[8]-=-. This last approach was subsequently extended to the entire spectrum of twist-two operators [9]. Finally, there is a recent proposal, also based on integrable twodimensional QFT, for a set of equatio... |

116 |
Exactly Marginal Operators And Duality
- Leigh, Strassler
- 1995
(Show Context)
Citation Context ...ntegrability. One possibility is to deform the N = 4 theory in such a way that the maximum amount of integrability is preserved. With this in mind, one can consider marginally β-deformed N = 4 theory =-=[11]-=-, which although not completely integrable has large integrable subsectors [12, 13], admitting an asymptotic Bethe ansatz. The β-deformed theory is obtained from the N = 4 theory by modifiying the sup... |

85 | Beauty and the twist: The Bethe ansatz for twisted - Beisert, Roiban - 2005 |

83 | Integrability for the Full Spectrum of Planar AdS/CFT - Gromov, Kazakov, et al. |

79 |
Tseytlin, “Gauge - string duality for superconformal deformations
- Frolov, Roiban, et al.
- 2005
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Citation Context ...he hamiltonian. Let us for convenience consider in detail the one-loop ansatz [12]. The discussion carries over unaltered to the asymptotic all-loop case, since the deformation enters in the same way =-=[20, 13]-=-. The marginally deformed one-loop SU(2) Bethe ansatz, with real deformation parameter β, is given by with cyclicity contraint and magnon energy e −2πiβL ( ) L uk + i/2 = uk − i/2 M∏ uk + i/2 k=1 M∏ j... |

75 |
Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B816
- Bajnok, Janik, et al.
- 2009
(Show Context)
Citation Context ...rom a thermodynamic Bethe ansatz calculation based on the quantum field theory of the string worldsheet [8]. This last approach was subsequently extended to the entire spectrum of twist-two operators =-=[9]-=-. Finally, there is a recent proposal, also based on integrable twodimensional QFT, for a set of equations determining the wrapping corrections to the entire spectrum of planar, gauge invariant operat... |

74 |
Lax pair for strings
- Frolov
(Show Context)
Citation Context ...and is obtained by deforming the S5 part of the background through a series of T-duality transformations and shifts of angular variables. The integrable structure of the string theory was analyzed in =-=[16]-=-. Wrapping calculations 1have been performed in the deformed theory for operators corresponding to one and two magnons [17, 18], and the first finite size correction to the giant magnon dispersion re... |

58 | Finite-size effects from giant magnons
- Arutyunov, Frolov, et al.
(Show Context)
Citation Context ... this again implies that the first wrapping correction at weak coupling for odd L at p = π should vanish 5 in an expansion around infinite volume. By contrast, the string theory finite-size result of =-=[27]-=- has no L-dependence beyond the argument of the exponential. Acknowledgments We are grateful to L. Freyhult, for useful comments and discussions, and to C. Gómez and especially R. Hernández for much h... |

52 |
Wrapping interactions and the genus expansion of the 2- point function of composite operators
- Sieg, Torrielli
(Show Context)
Citation Context ...ons are no longer valid (see for example [4]). In the gauge theory wrapping interactions need to be taken into account when the perturbative order reaches the length L of the gauge invariant operator =-=[5]-=- while in the string theory finite-size effects come from virtual corrections traveling around the worldsheet cylinder [6]. Recently, however, even wrapping effects have started to become manageable. ... |

51 | Deformations of N = 4 SYM and integrable spin chain models
- Berenstein, Cherkis
(Show Context)
Citation Context ...the maximum amount of integrability is preserved. With this in mind, one can consider marginally β-deformed N = 4 theory [11], which although not completely integrable has large integrable subsectors =-=[12, 13]-=-, admitting an asymptotic Bethe ansatz. The β-deformed theory is obtained from the N = 4 theory by modifiying the superpotential as Tr([X, Y ], Z) → e iπβ Tr(X, Y, Z) − e −iπβ Tr(Y, X, Z) . (1.1) The ... |

28 |
Giant magnons
- Bykov, Frolov
- 2008
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Citation Context ...elations. At a first glance they seem to behave slightly differently. For example, the ˜p = π, β = 1/2 magnon correction, given by (3.5), vanishes for all odd L, while the string theory correction of =-=[19]-=- does not do so. This difference seems to carry over to the N = 4 theory, since the dimension of the magnon operator at β = L−1 2L should coincide, by the symmetry, with the undeformed magnon energy a... |

27 |
Finite-size effects
- Fiamberti, Santambrogio, et al.
- 2008
(Show Context)
Citation Context ...ar variables. The integrable structure of the string theory was analyzed in [16]. Wrapping calculations 1have been performed in the deformed theory for operators corresponding to one and two magnons =-=[17, 18]-=-, and the first finite size correction to the giant magnon dispersion relation has been obtained on the string side [19]. In general, however, it seems difficult to construct a systematic method for o... |

25 |
Single impurity operators at critical wrapping order
- Fiamberti, Santambrogio, et al.
- 2009
(Show Context)
Citation Context ...ar variables. The integrable structure of the string theory was analyzed in [16]. Wrapping calculations 1have been performed in the deformed theory for operators corresponding to one and two magnons =-=[17, 18]-=-, and the first finite size correction to the giant magnon dispersion relation has been obtained on the string side [19]. In general, however, it seems difficult to construct a systematic method for o... |

20 |
Analytic continuation of the Mellin moments of deep inelastic structure functions
- Kotikov, Velizhanin
(Show Context)
Citation Context ...such unphysical states can be obtained by analytically continuing from the physical values of M. In fact the prescription used for analytically continuing the harmonic sums is the (−) prescription of =-=[24]-=-. and coincides with (3.10) at odd values of M. By contrast, usually the physical (+) prescription is used in N = 4 Yang-Mills, since it connects the physical, even M states. 2Indeed, at M = 1, the on... |

15 |
Twist-three at five loops, Bethe Ansatz and wrapping
- Beccaria, Forini, et al.
(Show Context)
Citation Context ...ned from (3.17), in contrast with (3.5). However, this does not give any useful information since then equation (3.17) is no longer valid. One could have started with an expression such as the one in =-=[25]-=-, giving the wrapping correction to twist-three operators, but in that case the one-magnon energy cannot be obtained by analytically continuing from the physical spectrum. For twist-three operators th... |

9 |
Anomalous dimensions of Wilson operators in N = 4 SYM theory, Phys
- Kotikov, Lipatov, et al.
(Show Context)
Citation Context ...)g 2r , (3.9) r=1 where the γr(M) can be conveniently expressed through a basis of harmonic sums, defined through M∑ (sgn(a)) Sa ≡ j ja , Sa1,...,an ≡ j=1 Setting M = 1 into the three-loop expressions=-=[23]-=- one finds [22], M∑ (sgn(a1)) j ja1 Sa2,...,an(j) . (3.10) j=1 γ(1) = 8g 2 − 32g 4 + 256g 6 + · · · , (3.11) which coincides with the expansion of the dispersion relation (3.1) at p = π. Furthermore s... |

7 |
The Factorized S-matrix of CFT/AdS,” JHEP 0505 (2005) 054, hep-th/0412188; N. Beisert and M. Staudacher, “Long-range psu(2,2—4) Bethe Ansatze for gauge theory and strings
- Staudacher
- 2006
(Show Context)
Citation Context ...ion of the planar spectra of N = 4 gauge theory and AdS5 × S5 string theory implied by the AdS/CFT correspondence [1]. First, the construction of the scattering matrix and the asymptotic Bethe ansatz =-=[2, 3]-=- turned reachable the spectrum of asymptotically long operators and infinitely fast strings in the supergravity background. For short operators, or strings with small charges it was shown that the Bet... |

5 |
Exact results in planar N = 1 superconformal Yang-Mills theory
- Mauri, Penati, et al.
(Show Context)
Citation Context ..., Y ], Z) → e iπβ Tr(X, Y, Z) − e −iπβ Tr(Y, X, Z) . (1.1) The deformation β can be complex in general, but we will limit ourselves to the study of real β, for which the theory remains superconformal =-=[14]-=-. The string theory dual of this theory was constructed in [15], and is obtained by deforming the S5 part of the background through a series of T-duality transformations and shifts of angular variable... |

4 |
Anomalous dimensions at twist-3 in the sl(2) sector of N = 4 SYM, JHEP 0706 (2007) 044, 0704.3570
- Beccaria
(Show Context)
Citation Context ...ors, but in that case the one-magnon energy cannot be obtained by analytically continuing from the physical spectrum. For twist-three operators the spectrum is given by harmonic sums evaluated at M/2 =-=[26]-=-, which do not seem to have meaningful values at odd values of M. So, for twist-three, and probably all odd twists, the physical, even M spectrum, seems to be completely disconnected from the unphysic... |

2 |
Wrapping at four loops in N = 4
- Fiamberti, Santambrogio, et al.
(Show Context)
Citation Context ...he four-loop anomalous dimension of the Konishi operator, which is the simplest case where wrapping effects are present, has been obtained both from perturbative computations on the gauge theory side =-=[7]-=- and from a thermodynamic Bethe ansatz calculation based on the quantum field theory of the string worldsheet [8]. This last approach was subsequently extended to the entire spectrum of twist-two oper... |