320 research outputs found
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
Minimal solution of the AdS/CFT crossing equation
We solve explicitly the crossing equation under sufficiently general
assumptions on the structure of the dressing phase. We obtain the BES/BHL
dressing phase as a minimal solution of the crossing equation and identify the
possible CDD factors.Comment: 4 pages, 2 figures. In v2: references added, introduction improved,
explanations in the text improved, typos corrected, section with explanation
of analytical properties of the dressing phase adde
Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
We continue the investigation of two-loop string corrections to the energy of
a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the
scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We
compute the generalized scaling function at two-loop order f_2(ell) both for
small and large values of ell matching the predictions based on the asymptotic
Bethe ansatz. In particular, in the small ell expansion, we derive an exact
integral form for the ell-dependent coefficient of the Catalan's constant term
in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman
diagrams we obtain an exact expression for the leading (ln ell) part of
f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2)
expansion. At large ell the string energy has a BMN-like expansion and the
first few leading coefficients are expected to be the same at weak and at
strong coupling. We provide a new example of this non-renormalization for the
term which is generated at two loops in string theory and at one-loop in gauge
theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for
the term of maximal transcendentality in f_2(ell) expanded at large ell. In the
second part of the paper we initiate the study of 2-loop finite size
corrections to the string energy by formally compactifying the spatial
world-sheet direction in the string action expanded near long fast-spinning
string. We observe that the leading finite-size corrections are of "Casimir"
type coming from terms containing at least one massless propagator. We consider
in detail the one-loop order (reproducing the leading Landau-Lifshitz model
prediction) and then focus on the two-loop contributions to the (1/ln S) term
(for J=0). We find that in a certain regularization scheme used to discard
power divergences the two-loop coefficient of the (1/ln S) term appears to
vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde
Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation
Recent advances in quantum information processing with trapped ions have
demonstrated the need for new ion trap architectures capable of holding and
manipulating chains of many (>10) ions. Here we present the design and detailed
characterization of a new linear trap, microfabricated with scalable
complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited
to this challenge. Forty-four individually controlled DC electrodes provide the
many degrees of freedom required to construct anharmonic potential wells,
shuttle ions, merge and split ion chains, precisely tune secular mode
frequencies, and adjust the orientation of trap axes. Microfabricated
capacitors on DC electrodes suppress radio-frequency pickup and excess
micromotion, while a top-level ground layer simplifies modeling of electric
fields and protects trap structures underneath. A localized aperture in the
substrate provides access to the trapping region from an oven below, permitting
deterministic loading of particular isotopic/elemental sequences via
species-selective photoionization. The shapes of the aperture and
radio-frequency electrodes are optimized to minimize perturbation of the
trapping pseudopotential. Laboratory experiments verify simulated potentials
and characterize trapping lifetimes, stray electric fields, and ion heating
rates, while measurement and cancellation of spatially-varying stray electric
fields permits the formation of nearly-equally spaced ion chains.Comment: 17 pages (including references), 7 figure
Review of AdS/CFT Integrability: An Overview
This is the introductory chapter of a review collection on integrability in
the context of the AdS/CFT correspondence. In the collection we present an
overview of the achievements and the status of this subject as of the year
2010.Comment: 31 pages, v2: reference added, references to other chapters updated,
v3: footnote 1 on location of references added, v4: minor changes, references
added, accepted for publication in Lett. Math. Phys, v5: minor corrections,
links to chapters updated, attached IntAdS.pdf with all chapters in one file,
see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or
http://www.phys.ethz.ch/~nbeisert/IntAdS.pd
Nonperturbative scales in AdS/CFT
The cusp anomalous dimension is a ubiquitous quantity in four-dimensional
gauge theories, ranging from QCD to maximally supersymmetric N=4 Yang-Mills
theory, and it is one of the best investigated observables in the AdS/CFT
correspondence. In planar N=4 SYM theory, its perturbative expansion at weak
coupling has a finite radius of convergence while at strong coupling it admits
an expansion in inverse powers of the 't Hooft coupling which is given by a
non-Borel summable asymptotic series. We study the cusp anomalous dimension in
the transition regime from strong to weak coupling and argue that the
transition is driven by nonperturbative, exponentially suppressed corrections.
To compute these corrections, we revisit the calculation of the cusp anomalous
dimension in planar N=4 SYM theory and extend the previous analysis by taking
into account nonperturbative effects. We demonstrate that the scale
parameterizing nonperturbative corrections coincides with the mass gap of the
two-dimensional bosonic O(6) sigma model embedded into the AdS_5xS^5 string
theory. This result is in agreement with the prediction coming from the string
theory consideration.Comment: 49 pages, 1 figure; v2: minor corrections, references adde
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