Maths HEP Lunchtime Seminars: Integrability, Transcendentality and Crossing
25 May 2007 13:00 in CM221
We analyze the all-loop Bethe ansatz for the sl(2) twist
operator sector of the N=4 gauge theory in the limit
of large spacetime spin at large but finite twist, and find a
novel all-loop scaling function. This function obeys the
Kotikov-Lipatov transcendentality principle and does not depend
on the twist.
We discuss possible phase factors for the
S-matrix, leading to modifications at four-loop order and beyond.
While these result in a four-loop breakdown of perturbative BMN-scaling,
transcendentality may be preserved in the universal scaling function.
One particularly natural dressing phase, unique up to one
constant, modifies the overall contribution of all terms
in the scaling function that contain odd zeta functions.
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.
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