On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.Comment: 116 pages, 11 figures, to be published in Advances in High Energy Physics, Special Issue on ''Gauge/String Duality'

Aspects of quantum integrability for pure spinor superstring in AdS(5)xS(5)

We consider the monodromy matrix for the pure spinor IIB superstring on $AdS_5\times S^5$ at leading order at strong coupling, in particular its variation under an infinitesimal and continuous deformation of the contour. Such variation is equivalent to the insertion of a local operator. Demanding the BRST-closure for such an operator rules out its existence, implying that the monodromy matrix remains contour-independent at the first order in perturbation theory. Furthermore we explicitly compute the field strength corresponding to the flat connections up to leading order and directly check that it is free from logarithmic divergences. The absence of anomaly in the coordinate transformation of the monodromy matrix and the UV-finiteness of the curvature tensor finally imply the integrability of the pure spinor superstring at the first order.Comment: 44 pages; 4 figure

Guidelines for Selecting Alternatives to Overreliance on Paraprofessionals

The Guidelines for Selecting Alternatives to Overreliance on Paraprofessionals is a field-tested schhol-based planning process. Support for the preparation of this article was provided by the United States Department of Education, Office of Special Education and Rehabilitative Services under the funding category, Model Demonstration Projects for Children and Youth with Disabilities, CFDA 84.324M (H324M02007), awarded to the Center on Disability and Community Inclusion at the University of Vermont. The contents of this document reflect the ideas and positions of the authors and do not necessarily reflect the ideas or positions of the U.S. Department of Education; therefore, no official endorsement should be inferred

The Paraprofessional Conundrum: Why We Need Alternative Support Strategies

This four-page article describes a conundrum facing schools utilizing paraprofessionals to support students receiving special education. It considers three factors: (a) asked to engage in teacher-type instructional roles, (b) trained and supervised for teacher-type instructional roles, and (c) compensation commensurate with teacher-type instructional roles across six combinations. Regardless of whether or not the factors are present or not it often leads to series of undesirable outcomes. The article suggest a series of alternatives

Quantized Strings and Instantons in Holography

We study worldsheet instantons in holographic type IIA backgrounds directly in string theory. The first background is a dimensional reduction of AdS$_7\times S^4$ and is dual to the maximally supersymmetric Yang-Mills theory on $S^5$. The second background is AdS$_4\times \mathbf{C}P^3$ dual to ABJM in the type IIA limit. We compute the one-loop partition function of the fundamental string in these backgrounds and show that the result is in exact agreement with field theory predictions. We argue that for higher rank instantons, the string partition function takes a product form of the single instanton partition function times the contribution of two orbifolds on the worldsheet. We determine the orbifold factor to be $n^{-3/2}$ where $n$ is the instanton rank. With this result, we reproduce the series of non-perturbative corrections in $\alpha'$ to the planar $S^5$ free energy. When studying the worldsheet instanton partition function on $\mathbf{C}P^3$, we encounter twelve fermionic and twelve bosonic zero modes. By deforming the ABJM theory, the zero-modes are lifted and consequently the tower of worldsheet instantons can be evaluated and matched to known results in the QFT. As a by-product, we determine a series of higher rank instanton corrections to the free energy of the mass-deformed and orbifolded ABJ(M) theory.Comment: 35 pages. v2: Minor correction