42 research outputs found
A next-to-leading Luescher formula
We propose a next-to-leading Luescher-like formula for the finite-size
corrections of the excited states energies in integrable theories. We
conjecture the expressions of the corrections for both the energy and the
particles' rapidities by interpreting the excited states as momenta-dependent
defects. We check the resulting formulas in some simple relativistic model and
conjecture those for the AdS5/CFT4 case.Comment: 19 pages, 2 figures;v2: minor corrections, clarifications and a
reference adde
Quantum Strings and the AdS4/CFT3 Interpolating Function
The existence of a nontrivial interpolating function h(\lambda) is one of the
novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At
strong coupling, most of the investigation of semiclassical effects so far has
been for strings in the AdS4 sector. Several cutoff prescriptions have been
proposed, leading to different predictions for the constant term in the
expansion h(\lambda)=\sqrt{\lambda/2} + c + ... . We calculate quantum
corrections for giant magnons, using the algebraic curve, and show by comparing
to the dispersion relation that the same prescriptions lead to the same values
of c in this CP3 sector. We then turn to finite-J effects, where a comparison
with the Luescher F-term correction shows a mismatch for one of the three sum
prescriptions. We also compute some dyonic and higher F-terms for future
comparisons.Comment: 30 pages, 1 figure, 1 table. v2 has minor improvements to the text,
and extra references. v3 has further textual changes, version to appear in
JHE
12 loops and triple wrapping in ABJM theory from integrability
Adapting a method recently proposed by C. Marboe and D. Volin for =4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling
expansion of the spectrum of anomalous dimensions in the -like sector of
planar =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 , 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 Pad\'e
extrapolation of the 12-loop result nicely agrees with the available
Thermodynamic Bethe Ansatz data in a relatively wide range of values of the
coupling. A Mathematica notebook with a selection of results is attached.Comment: 31 pages, 1 figure. A Mathematica notebook with a selection of
results is attached (please download the compressed file "Results.nb" listed
under "Other formats"). v2: typos corrected; more precise checks of the
results; an earlier incorrect version of the figure was replaced. Published
in JHE
The full Quantum Spectral Curve for
The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type
IIA superstring theory on , is accessible at finite coupling
using integrability. Starting from the results of [arXiv:1403.1859], we study
in depth the basic integrability structure underlying the spectral problem, the
Quantum Spectral Curve. The new results presented in this paper open the way to
the quantitative study of the spectrum for arbitrary operators at finite
coupling. Besides, we show that the Quantum Spectral Curve is embedded into a
novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and
leads to exact Bethe Ansatz equations. The discovery of this algebraic
structure, more intricate than the one appearing in the case,
could be a first step towards the extension of the method to .Comment: 43 + 27 pages, 7 figures. v4: text improved, more details and App D
included. This is the same as the published version JHEP09(2017)140, with
small typos corrected in App
Real and Virtual Bound States in L\"uscher Corrections for CP3 Magnons
We study classical and quantum finite-size corrections to giant magnons in
AdS_4 x CP^3 using generalised L\"uscher formulae. L\"uscher F-terms are
organised in powers of the exponential suppression factor exp(-Delta/2h)^m, and
we calculate all terms in this series, matching one-loop algebraic curve
results from our previous paper arXiv:1006.2174. Starting with the second term,
the structure of these terms is different to those in AdS_5 x S^5 thanks to the
appearance of heavy modes in the loop, which can here be interpreted as
two-particle bound states in the mirror theory. By contrast, physical bound
states can represent dyonic giant magnons, and we also calculate F-terms for
these solutions. L\"uscher mu-terms, suppressed by exp(-Delta/E), instead give
at leading order the classical finite-size correction. For an elementary dyonic
giant magnon, we recover the correction given by arXiv:0903.3365. We then
extend this to calculate the next term in 1/h, giving a one-loop prediction.
Finally we also calculate F-terms for the various composite giant magnons, RP^3
and `big', again finding agreement to all orders.Comment: 33 pages and 3 figures. v3 adds new section treating F-terms of all
orders; version to appear in J. Phys.