6,395 research outputs found
Spinning strings in the -deformed Neumann-Rosochatius system
The sigma-model of closed strings spinning in the -deformation of
leads to an integrable deformation of the
one-dimensional Neumann-Rosochatius mechanical system. In this article we
construct general solutions to this system that can be written in terms of
elliptic functions. The solutions correspond to closed strings with
non-constant radii rotating with two different angular momenta in an
-deformed three-sphere. We analyse the reduction of the elliptic
solutions for some limiting values of the deformation parameter. For the case
of solutions with constant radii we find the dependence of the classical energy
of the string on the angular momenta as an expansion in the 't Hooft coupling.Comment: 17 pages. Latex. v2: Additional references. v3: Minor changes and
updated reference
Holographic correlation functions of hexagon Wilson loops with one local operator
We consider the ratio of the correlation function of an hexagon light-like
Wilson loop with one local operator over the expectation value of the Wilson
loop within the strong-coupling regime of the AdS/CFT correspondence. We choose
the hexagon Wilson loop within a class of minimal solutions obtained by cutting
and gluing light-like quadrangle loops. These surfaces do not have an
interpretation in terms of dual scattering amplitudes but they still exhibit
general features of the mixed correlation function. In the case of a regular
null hexagon conformal symmetry constrains the space-time dependence of the
correlator up to a function of three conformal cross-ratios. We obtain the
leading-order contribution to the correlation function in the semiclassical
approximation of large string tension, and express the result in terms of three
conformal ratios in the case where the local operator is taken to be the
dilaton. We include the analysis of an irregular Wilson loop obtained after a
boost of the regular hexagon.Comment: 12 pages. Latex. v2: Reference added. v3: Added clarifications,
published versio
Elliptic solutions in the Neumann-Rosochatius system with mixed flux
Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS
three-form fluxes are described by a deformation of the one-dimensional
Neumann-Rosochatius integrable system. In this article we find general
solutions to this system that can be expressed in terms of elliptic functions.
We consider closed strings rotating either in S^3 with two different angular
momenta or in AdS_3 with one spin. In order to find the solutions we will need
to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system
to include the contribution from the flux. In the limit of pure NS-NS flux,
where the problem can be described by a supersymmetric WZW model, we find exact
expressions for the classical energy in terms of the spin and the angular
momenta of the spinning string.Comment: 18 pages. Latex. v2: Extended discussions, corrected misprints and
added reference. Published versio
Spinning strings in AdS_3 x S^3 with NS-NS flux
The sigma model describing closed strings rotating in AdS_3 x S^3 is known to
reduce to the one-dimensional Neumann-Rosochatius integrable system. In this
article we show that closed spinning strings in AdS_3 x S^3 x T^4 in the
presence of NS-NS three-form flux can be described by an extension of the
Neumann-Rosochatius system. We consider closed strings rotating with one spin
in AdS_3 and two different angular momenta in S^3. For a class of solutions
with constant radii we find the dependence of the classical energy on the spin
and the angular momenta as an expansion in the square of the 't Hooft coupling
of the theory.Comment: 14 pages. Latex. v2: Equations (3.19) and (3.28) corrected and
reference added. v3: Expanded discussion on the WZW limit and additional
references. Published version. v4: Misprints correcte
The Effect of Assessment Method on End of Course Geometry and Algebra Achievement
The purpose of this dissertation was to add to the existing research concerning the effects of assessment on mathematics achievement. The effects by gender or SES of students enrolled in school districts that used a commercial assessment versus school districts that used local assessments on mathematics achievement as measured by the end of course algebra I exam or end of course geometry exam.
This quantitative, causal comparative study was performed in six rural high schools in the Arkansas River Valley. The high schools had an approximate 700-student population of which 53% were categorized as free and/or reduced lunch and 51% were female. The end of course algebra I exam and geometry exam, given to all students enrolled in each course, was used as the instrument to measure mathematics achievement.
Included in the sample were all first time 9th graders for algebra I and first time 10th graders for geometry. Exactly 711 students comprised the sample. The students were classified according to their gender, SES, and the type of assessment method. The two categories of assessment were student enrolled in a course where The Learning Institute (TLI) interim assessment was used versus where a locally made assessment was used. Four 2 x 2 factorial ANCOVA’s were used to analyze the data for all hypothesis. No significant interaction effects were observed between students for assessment type and gender or assessment type and SES. For algebra achievement, there were significant difference found for assessment type but not for the main effects of gender or SES. For geometry, there were significant differences found for the main effects of assessment type, gender, and SES
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