Surprisingly Simple Spectra

The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so that the classical dimension of these operators is O(N). At large N these two column operators mix with each other but are decoupled from operators with $n\ne 2$ columns. The planar approximation does not capture the large N dynamics. For operators built with 2, 3 or 4 impurities the dilatation operator is explicitly evaluated. In all three cases, in a certain limit, the dilatation operator is a lattice version of a second derivative, with the lattice emerging from the Young diagram itself. The one loop dilatation operator is diagonalized numerically. All eigenvalues are an integer multiple of $8g_{YM}^2$ and there are interesting degeneracies in the spectrum. The spectrum we obtain for the one loop anomalous dimension operator is reproduced by a collection of harmonic oscillators. This equivalence to harmonic oscillators generalizes giant graviton results known for the BPS sector and further implies that the Hamiltonian defined by the one loop large $N$ dilatation operator is integrable. This is an example of an integrable dilatation operator, obtained by summing both planar and non-planar diagrams.Comment: 34 page

Strings on Bubbling Geometries

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.Comment: 41 pages, 12 figures, published version in JHE

Giant Graviton Oscillators

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.Comment: 72 page

Dielectric 5-Branes and Giant Gravitons in ABJM

We construct a supersymmetric NS5-brane wrapped on a twisted 5-sphere expanding in the $CP^3$ in $AdS_4\times CP^3$, with D0-brane charge. This configuration provides a realization of the stringy exclusion principle in terms of giant D0-branes. In the maximal case the twisted 5-sphere reduces to a $CP^2$ and its energy can be accounted for both by a bound state of $k$ D4-branes wrapping the $CP^2$ and a bound state of $N$ D0-branes, a realization on the gravity side of the symmetry of Young diagrams with $N$ rows and $k$ columns. We discuss some generalizations of this configuration in M-theory carrying angular momentum, some of them with an interpretation as giant gravitons. We provide the microscopical description that allows to explore the region of finite 't Hooft coupling.Comment: 26 pages, reference adde

Esc Anna Nery

AbstrAct Objectives: To conduct a reflective analysis of knowledge acquired concerning the use of acupuncture as a complementary treatment to treat individuals with hypertension; and discuss the contributions of acupuncture to nursing diagnoses among hypertensive individuals and those contributions' implications for nursing practice. Methods: Integrative literature review presenting a theoretical and philosophical reflection regarding the topic in the last five years. Results: The findings were organized into two categories: primary evidence of the practice as complementary treatment to care provided to hypertensive patients; and contributions to care delivery according to nursing-diagnosis based interventions. Conclusion: Evidence shows the potential of acupuncture as complementary treatment and the potential for it to be included in the nursing care provided to hypertensive individuals. Keywords: Hypertension; Acupuncture Therapy; Nursing; Nursing Diagnosis. resumo Objetivos: Realizar uma análise reflexiva sobre o conhecimento produzido acerca da utilização da acupuntura como tratamento complementar à saúde de pessoas com hipertensão; e discutir as contribuições da acupuntura sobre diagnósticos de enfermagem em pessoas com hipertensão e suas implicações à prática do enfermeiro. Métodos: Reflexão teórica a partir de revisão integrativa da literatura sobre a temática nos últimos cinco anos. Resultados: Os achados foram organizados e discutidos em duas categorias que apresentam as principais evidências da prática como tratamento complementar à saúde de pessoas hipertensas e suas contribuições para o cuidado a partir da intervenção sobre diagnósticos de enfermagem. Conclusão: Existem evidências que apontam o potencial da acupuntura no tratamento complementar de saúde indicando possiblidade de sua inserção no cuidado de enfermagem a pessoas hipertensas. Palavras-chave: Hipertensão; Terapia por acupuntura; Enfermagem; Diagnóstico de Enfermagem. resumen Objetivos: Realizar un análisis reflexivo de los conocimientos producidos por el uso de la acupuntura como tratamiento complementario para la salud de las personas con hipertensión; y discutir las contribuciones de acupuntura en diagnósticos de enfermería en personas con hipertensión y sus implicaciones para la práctica de enfermería. Métodos: Reflexión teórica a partir de una revisión integradora de la literatura sobre el tema en los últimos cinco años. Resultados: Se organizaron los resultados en dos categorías que analizan las evidencias principales de la práctica como un tratamiento complementario para la salud de las personas hipertensas y sus contribuciones la intervención sobre los diagnósticos de enfermería. Conclusión: Hay evidencia el potencial de la acupuntura como un tratamiento complementario de salud que indica la posibilidad de su inclusión en los cuidados de enfermería para las personas hipertensas