Two-loop commuting charges and the string/gauge duality

We briefly review the status quo of the application of integrable systems techniques to the AdS/CFT correspondence in the large charge approximation, a rapidly evolving topic. Intricate string and gauge computations of, respectively, energies and scaling dimensions agree at the one and two-loop level, but disagree starting from three loops. To add to this pattern, we present further computations which demonstrate that for folded and circular spinning strings the full tower of infinitely many hidden commuting charges, responsible for the integrability, also agrees up to two, but not three, loops.Comment: 12 pages, Latex, contribution to 5th International Workshop on Lie Theory and Its Applications in Physics, Varna, Bulgaria, 16-22 Jun 2003; v2: references adde

Redirection of the immune response to Staphylococcus aureus biofilm infection

Staphylococcus aureus (S. aureus) is a leading cause of community- and healthcare-associated infections and has a propensity to form biofilms. Biofilm infections are recalcitrant to host immune-mediated clearance as well as antibiotics, making them exceptionally difficult to eradicate. The biofilm environment has been shown to skew the host immune response towards an anti-inflammatory phenotype, characterized by alternatively activated macrophages, recruitment of myeloid-derived suppressor cells (MDSCs), and minimal neutrophil and T cell infiltrates. Our laboratory has attempted to redirect the host immune response towards one that would favor bacterial clearance by employing strategies to augment pro-inflammatory mechanisms. One such approach was to utilize lipopolysaccharide (LPS), which was expected to promote pro-inflammatory activation of peripheral immune cells infiltrating the biofilm and subsequent clearance of infection. This theory was partially correct, as pro-inflammatory cytokines in the serum were significantly increased, and peripheral immune cells in the blood were more effective at killing S. aureus ex vivo following LPS treatment; however biofilm infection was exacerbated. Specifically, bacterial titers increased nearly 2-log with administration of LPS, and although infiltration of Ly6G+Ly6C+ MDSCs was decreased, a new population of Ly6GintLy6C+ cells appeared. Additionally, both Ly6G+Ly6C+ and Ly6GintLy6C+ populations were more suppressive with LPS treatment, partially explaining the expansion of S. aureus biofilm burdens. This study highlights the resilient nature of S. aureus biofilm infections to influence the immune response, particularly through MDSCs, even in the face of a strong pro-inflammatory stimulus. Gaining a better understanding of the mechanisms that cause this ineffective host immune response to staphylococcal biofilms is a necessary step towards eradicating these debilitating infections

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio

Magic identities for conformal four-point integrals

We propose an iterative procedure for constructing classes of off-shell four-point conformal integrals which are identical. The proof of the identity is based on the conformal properties of a subintegral common for the whole class. The simplest example are the so-called `triple scalar box' and `tennis court' integrals. In this case we also give an independent proof using the method of Mellin--Barnes representation which can be applied in a similar way for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of contact terms. Typo correcte

On the Scattering Phase for AdS_5 x S^5 Strings

We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x S^5 apparently solving Janik's crossing relation.Comment: 9 pages, v2: revised conclusions about agreement with perturbative string theory; minor changes, v3: resolution to above problems indicated, to appear in Mod. Phys. Lett.

Decoupling limits of N=4 super Yang-Mills on R x S^3

We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with gauge group SU(N). These decoupling limits lead to decoupled theories that are much simpler than the full N=4 SYM but still contain many of its interesting features. The decoupling limits correspond to being in a near-critical region, near a point with zero temperature and critical chemical potentials. The new decoupling limits are found by generalizing the limits of hep-th/0605234 to include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM but also the chemical potentials corresponding to the SO(4) symmetry. In the decoupled theories it is possible to take a strong coupling limit in a controllable manner since the full effective Hamiltonian is known. For planar N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable spin chains. We study the thermodynamics of the decoupled theories and find the Hagedorn temperature for small and large values of the effective coupling. We find an alternative formulation of the decoupling limits in the microcanonical ensemble. This leads to a characterization of certain regimes of weakly coupled N=4 SYM in which there are string-like states. Finally, we find a similar decoupling limit for pure Yang-Mills theory, which for the planar limit leads to a fully integrable decoupled theory.Comment: 48 pages, 1 figure; added references, published versio

On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory

We consider the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z is a complex scalar and \psi is a component of gaugino. We show that this state corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the antiferromagnetic state in the su(2) sector. We find perturbative expansions of the energy of this state in both weak and strong 't Hooft coupling regimes using asymptotic gauge theory Bethe ansatz equations. We also discuss a possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late

Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM

We present the perturbative Yangian symmetry at next-to-leading order in the su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators, the bi-local Yangian charges receive corrections acting on several neighboring sites. We confirm that the bi-local Yangian charges satisfy the necessary conditions: they transform in the adjoint of su(2|1), they commute with the dilatation generator, and they satisfy the Serre relations. This proves that the sector is integrable at two loops.Comment: 13 pages, v2: minor correction

Character Expansion Methods for Matrix Models of Dually Weighted Graphs

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large $N$ limit of the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into the text in Pictex commands. (Two minor math typos corrected. Acknowledgements added.

Planar N=4 Gauge Theory and the Hubbard Model

Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N=4 gauge theory in the su(2) sector to at least three-loop order, while exhibiting BMN scaling to all orders in perturbation theory. Here we identify this spin chain as an approximation to an integrable short-ranged model of strongly correlated electrons: The Hubbard model.Comment: 35 pages, 2 figures; v2: typos and references fixed, published versio