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12 loops and triple wrapping in ABJM theory from integrability | | Lorenzo Anselmetti
; Diego Bombardelli
; Andrea Cavaglià
; Roberto Tateo
; | | Date: |
30 Jun 2015 | | Abstract: | Adapting a method recently proposed by C. Marboe and D. Volin for ${cal
N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling
expansion for anomalous dimensions of operators in the $sl(2)$-like sector of
planar $mathcal{N}$=6 super-Chern-Simons. The method relies on the Quantum
Spectral Curve formulation of the problem and the expansion is written in terms
of the interpolating function $h(lambda)$, with coefficients expressible as
combinations of Euler-Zagier sums with alternating signs. We present explicit
results up to 12 loops (six nontrivial orders) for various twist L=1 and L=2
operators, corresponding to triple and double wrapping terms, respectively,
which are beyond the reach of the Asymptotic Bethe Ansatz as well as
L"uscher’s corrections. The algorithm works for generic values of L and S and
in principle can be used to compute arbitrary orders of the weak coupling
expansion. For the simplest operator with L=1 and spin S=1, the 12-loop
computation matches very well with the available Thermodynamic Bethe Ansatz
data. The good agreement between the Pad’e extrapolated result and TBA
numerics goes even beyond the expected radius of convergence. | | Source: | arXiv, 1506.9089 | | Services: | Forum | Review | PDF | Favorites | |
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