Matrix Reduction and the su(2|2) superalgebra in AdS/CFT

We study the supersymmetry generators Q, S on the 1-loop vectorless sector of N=4 Super Yang-Mills, by reduction to the plane-wave matrix model. Using a coherent basis in the su(2|2) sector, a comparison with the algebra given by Beisert in nlin/0610017 is presented, and some parameters (up to one-loop) are determined. We make a final comparison of these supercharges with the results that can be obtained from the string action by working in the light-cone-gauge and discretizing the string.Comment: 20 pages, no figures v2: Typos corrected, references adde

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' giant magnons we obtain new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and minor clarification

Searching for the G516T Polymorphism on the CYP2B6 gene in HIV-1Patients

Poster presented at the International Young Researchers in Life Sciences Conference. Pasteur Institute, Paris, France, 26-28 May 2014

Moduli Dynamics of AdS_3 Strings

We construct a general class of solutions for a classical string in AdS_3 spacetime. The construction is based on a Pohlmeyer type reduction, with the sinh-Gordon model providing the general N-soliton solutions. The corresponding exact spiky string configurations are then reconstructed through the inverse scattering method. It is shown that the string moduli are determined entirely by those of the solitons.Comment: 22 pages, no figures; references adde

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian

This paper studies giant magnons in CP3, which in all known cases are old solutions from S5 placed into two- and three-dimensional subspaces of CP3, namely CP1, RP2 and RP3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the relevant 'vacuum' point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finite-J solutions, and use these to compare string solutions to giant magnons in the algebraic curve.Comment: 17 pages (plus appendices) and 1 figure. v2 has new discussion of placing finite-J giant magnons into CP^3, adds many references, and corrects a few typo

Dressed Giant Magnons on CP^3

A new example of AdS/CFT duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory has recently been provided by ABJM. By now a number of papers have considered particular giant magnon classical string solutions in the CP^3 background, corresponding to excitations in the spin chain picture of the dual field theory. In this paper we apply the CP^3 = SU(4)/S(U(3) x U(1)) dressing method to the problem of constructing general classical string solutions describing various configurations of giant magnons. As a particular application we present a new giant magnon solution on CP^3. Interestingly the dressed solution carries only a single SO(6) charge, in contrast with the dyonic magnons found in previous applications of the dressing method.Comment: 13 pages, harvmac; v3: fixed misstatement of the dispersion relation(!), v3: typos fixed and a few clarifying remarks adde