Dual superconformal symmetry fromAdS5×S5superstring integrability

Abstract

We discuss 2d duality transformations in the classical AdS 5 × S 5 superstring and their effect on the integrable structure. T-duality along four directions in the Poincaré parametrization of AdS 5 maps the bosonic part of the superstring action into itself. On the bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2, 4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transformation of the bosonic components of the current with a transformation on the fermionic ones. At the level of the action, this symmetry can be seen by combining the bosonic duality transformation with a similar one applied to part of the fermionic superstring coordinates. As a result, the full superstring action is mapped into itself, albeit in a different κ-symmetry gauge. One implication is that the dual model has the same superconformal symmetry group as the original one, and this may be seen as a consequence of the integrability of the superstring. The invariance of the Lax connection under the duality implies a map on the full set of conserved charges that should interchange some of the Noether (local) charges with hidden (non-local) ones and vice versa.

Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes

“…Dual superconformal symmetry [1,2] has played an important role in understanding the structure of planar four-dimensional N = 4 super-Yang-Mills (sYM) theory at both strong [3][4][5][6] and weak coupling [7][8][9][10]. In particular, the closure of the original and dual superconformal symmetries forms an infinite-dimensional Yangian symmetry [11], which has been extremely useful in determining the planar amplitudes of four-dimensional N = 4 sYM [12][13][14][15][16][17][18].…”

T‐Duality, dual conformal symmetry and integrability for strings on AdS5 × S5

“…Conversely the JQ terms must stay in place and the automorphism should be independent of z. Altogether this is achieved by the following transformation [21] A(z) = Ω z (A(z)),…”

“…Furthermore, what is the image of the integrable structure under T-duality? It turns out that both questions have a common answer [18,21,22] (see also [23]). The closure of the algebra is the integrable structure, and the latter is mapped to itself but in a non-trivial manner.…”

“…Thus the simplicity of planar scattering amplitudes is indeed closely related to the integrability of planar AdS/CFT. This note is a review of the works [9,18,21] outlining T-duality for superstrings on AdS 5 × S 5 and how the integrable structure transforms under it. We extend the previous works slightly by making the mapping of the integrable charges more explicit.…”

“…Acknowledgements I thank Ricardo Ricci, Arkady Tseytlin and Martin Wolf for the fruitful collaboration in the article [21] on which this work is based to a large extent. I acknowledge hospitality at the DESY Workshop on …”