Geometry of massless scattering in integrable superstring

Abstract

We consider the action of the q-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable AdS 2 ×S 2 ×T 6 type IIB superstring theory. The boost generator acts non-trivially on the R-matrix, confirming the existence of a non-relativistic rapidity γ with respect to which the R-matrix must be of difference form. We conjecture that from a massless AdS/CFT integrable relativistic R-matrix one can obtain the parental massless non-relativistic R-matrix simply by replacing the relativistic rapidity with γ. We check our conjecture in ordinary (undeformed) AdS n × S n × T 10−2n , n = 2, 3. In the case n = 3, we check that the matrix part and the dressing factor -up to numerical accuracy for real momenta -obey our prescription. In the n = 2 case, we check the matrix part and propose the non-relativistic dressing factor. We then start a programme of classifying R-matrices in terms of connections on fibre bundles. The conditions obtained for the connection are tested on a set of known integrable R-matrices.

The effectiveness of relativistic invariance in AdS3

“…In this section we give a full proof of the fact discovered in [27] that the non-relativistic massless sector of string theory on AdS 3 × S 3 × T 4 can be entirely recast into a difference-form in terms of the new variable γ = log tan p 4 .…”

“…In this paper, we use relativistic invariance to calculate finite size corrections due to massless excitations in integrable AdS 3 /CFT 2 in two settings. Firstly, building on the hidden-relativistic invariance found in [27], we construct the exact in α ′ TBA for AdS 3 R-R charge backgrounds, and show how it reduces to the low-energy TBA of [29]. We use this exact TBA to show that the BMN vacuum does not receive finite size corrections.…”

“…In this section we use the hidden relativistic invariance found in [27] to analyse the exact dressing factor, ABA and TBA for the massless sector of the R-R AdS 3 theory. 4…”

“…Since the exact massless S matrix has to be of difference form [27], we see that one cannot add χ AFS as a CDD factor to θ •• min . More generally, requiring such a difference form on the c r,s expansion of dressing phases…”

“…In this paper we exploit the appearance of relativistic invariance in integrable AdS 3 holography in two complementary contexts. Firstly, in the R-R theory (k = 0), it was recently found in [27] that the massless S matrix can be written in a difference form when expressed in terms of unconventional rapidity variables γ = log tan p 4 .…”