Spinning strings in the η\eta-deformed Neumann-Rosochatius system

The sigma-model of closed strings spinning in the $\eta$-deformation of $AdS_{5} \times S^{5}$ 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 $\eta$-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

Cuantificación de 17B-Estradiol proveniente de Efuentes Hospitalarios mediante Cromatografía de líquidos de alta resolución y determinación de Cinética de Degradación

En este trabajo de investigación se efectuó la determinación de 17β-estradiol en el afluente y efluente de una planta de tratamiento de agua residual de un hospital, la metodología incluye una extracción en fase sólida para la recuperación del analito en la muestra empleando el cartucho Oasis HLB, posteriormente se procedió a la cuantificación de esta hormona por un método analítico desarrollado por Cromatografía de Líquidos de Alta Resolución validado, el cual se basó en la separación de la hormona utilizando la columna cromatográfica Symmetry C18 3.0×250 mm×5µm Waters con detección UV a 280 nm para lo cual se empleó una fase móvil compuesta por acetonitrilo: agua en proporción 60:40 con 0.1% de ácido fórmico. La curva de calibración de 17β-estradiol se realizó en un rango de 100μg/L-5000 μg/L, mostrando una linealidad con un coeficiente de determinación igual a 0.9997.El límite de detección fue de 50 μg/L y el límite de cuantificación de 100 μg/L. El método analítico resultó lineal, preciso, específico y exacto en el desarrollo de su validación en el intervalo de las concentraciones estudiadas. Para la cuantificación de 17β-estradiol en el agua residual del hospital, se realizaron 11 muestreos semanales en los meses comprendidos de abril a junio del 2013. El analito se extrajo y concentró a través de cartuchos Oasis HLB. El promedio de los recobros obtenidos para el afluente fueron de 82.66%-104.52% y del efluente de 86.57-99.25%. La cuantificación por CLAR mostró la presencia de 17β-estradiol con niveles de concentración en el afluente de 18.81-60.57 µg /L y en el efluente de 5.29-54.63 µg/L

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

Minimal surfaces with mixed three-form flux

We study minimal area world sheets ending on two concentric circumferences on the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes. We solve the problem by reducing the system to a one-dimensional integrable model. We find that the NS-NS flux term either brings the surface near to the boundary or separates the circumferences. In the limit of pure NS-NS flux the solution adheres to the boundary in the former case and the outer radius diverges in the latter. We further construct the underlying elliptic spectral curve, which allows us to analyze the deformation of other related minimal surfaces. We show that in the regime of pure NS-NS flux the elliptic curve degenerates.Comment: 15 pages. Latex. v2: Title changed together with minor updates to emphasize that minimal area surfaces in the presence of mixed fluxes are found. v3: Published versio

Pulsating strings with mixed three-form flux

Circular strings pulsating in $AdS_3 \times S^3 \times T^4$ with mixed R-R and NS-NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in $AdS_{3}$ with pure NS-NS three-form flux, where the action reduces to the $SL(2,\mathbb{R})$ WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow by Maldacena and Ooguri. We use our elliptic solutions in $AdS_{3}$ to extend the dispersion relation beyond the limit of pure NS-NS flux.Comment: 10 pages. Late

The SU(2)SU(2) Wess-Zumino-Witten spin chain sigma model

Classical strings propagating in $AdS_{3}\times S^{3}\times T^{4}$ supported with Neveu-Schwarz-Neveu-Schwarz flux are described by a Wess-Zumino-Witten model. In this note, we study the emergence of their semiclassical $SU(2)$ spectrally flowed sectors as the Landau-Lifshitz limit of the underlying quantum spin chain. We consider the propagator in the coherent state picture, and find that the time interval is discretized proportionally to the lattice spacing. In the Landau-Lifshitz limit, where both time and space become continuous, we derive a path integral representation of the propagator for each spectrally flowed sector. We prove that the arbitrariness of the global phase of coherent states is mapped to the gauge freedom of the $B$-field in the classical action. We show that higher order corrections in the Landau-Lifshitz limit are suppressed by inverse powers of the 't Hooft coupling.Comment: 10 pages, Latex. v2: Published version. v3: Acknowledgement adde

Determination of the Number of Epoxides Groups by FTIR-HATR and Its Correlation with 1H NMR, in Epoxidized Linseed Oil

Artículo completo publicadoBy varying the conditions of the epoxidation reaction, samples of epoxidized linseed oil with different epoxidation degrees were obtained. The epoxidation of linseed oil was carried out by the formation of peracetic acid in situ using acetic acid, hydrogen peroxide solution, Amberlite IR-120H as the catalyst, and toluene as solvent. The quantification of the number of epoxides was carried out by 1H-NMR and the values obtained were correlated with the absorbance of the epoxy group signal in the FTIR-HATR spectrum. The method used to quantify the absorbance of the epoxy group signal by FTIR-HATR is based on the analysis of two regions: the area between 765-854 cm-1, and the net absorbance at 821 cm-1. Both signals analysis showed high linear correlation coefficients corroborating that this methodology represents an easy, fast, and reliable technique in the quantification of epoxides in natural oils.The authors thank to project SIEA-UAEM 4965/2020CIB, CONACYT for the Master fellowship, and to M.C. María de las Nieves Zavala from CCIQS, UAEM-UNAM for her technical support in the 1H-NMR analysis, through the intern project of the CCIQS SHL-2018