Transcendentality and crossing

Abstract

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 AdS 5 × S 5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.1 While finalizing our manuscript we were informed that this computation [12] has been completed.

The Bethe ansatz equations for reflecting magnons

“…As shown in [23][24][25], this algebra is strong enough to completely determine the form of the Smatrix up to an overall multiplicative scalar factor. In Ref.…”

“…Firstly, the S-matrix (4)- (6) does not depend on the difference of the spectral parameters and in fact, it is equivalent to Shastry's R-matrix [24,27] embedding the one-dimensional Hubbard model [28]. This feature leads us to consider the approach proposed in [29,30] and subsequently considered by other authors [31].…”

“…In this sense, the scattering of a particle with the boundaries is described by the so-called boundary S-matrices or reflection matrices, and compatibility between the boundary scattering and the bulk integrability demands the reflection matrices to satisfy reflection equations (11), (12). From the perspective of the AdS 5 × S 5 string theory, the scattering amplitudes of the world-sheet excitations are described by a S-matrix invariant relative to the centrally extended su(2|2) ⊗ su(2|2) superalgebra [23,24]. The corresponding S-matrix is fully constrained by this symmetry algebra, up to an overall multiplicative scalar factor, and it is explicitly given by…”

Twist 3 of the sector of SYM and reciprocity respecting evolution

“…The last term in (2.9d), with ¬ ¿ , is the contribution from the dressing factor that appears in the BAE at the fourth loop [22].…”

Constructing the AdS/CFT dressing factor

“…Recently, using the crossing constraint [16] and transcendentality principles [17], the full form of the scalar factor was conjectured from the string [18] and gauge [19] theory points of view.…”