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

Activin and TGFβ use diverging mitogenic signaling in advanced colon cancer.

BackgroundUnderstanding cell signaling pathways that contribute to metastatic colon cancer is critical to risk stratification in the era of personalized therapeutics. Here, we dissect the unique involvement of mitogenic pathways in a TGFβ or activin-induced metastatic phenotype of colon cancer.MethodMitogenic signaling/growth factor receptor status and p21 localization were correlated in primary colon cancers and intestinal tumors from either AOM/DSS treated ACVR2A (activin receptor 2) -/- or wild type mice. Colon cancer cell lines (+/- SMAD4) were interrogated for ligand-induced PI3K and MEK/ERK pathway activation and downstream protein/phospho-isoform expression/association after knockdown and pharmacologic inhibition of pathway members. EMT was assessed using epithelial/mesenchymal markers and migration assays.ResultsIn primary colon cancers, loss of nuclear p21 correlated with upstream activation of activin/PI3K while nuclear p21 expression was associated with TGFβ/MEK/ERK pathway activation. Activin, but not TGFβ, led to PI3K activation via interaction of ACVR1B and p85 independent of SMAD4, resulting in p21 downregulation. In contrast, TGFβ increased p21 via MEK/ERK pathway through a SMAD4-dependent mechanism. While activin induced EMT via PI3K, TGFβ induced EMT via MEK/ERK activation. In vivo, loss of ACVR2A resulted in loss of pAkt, consistent with activin-dependent PI3K signaling.ConclusionAlthough activin and TGFβ share growth suppressive SMAD signaling in colon cancer, they diverge in their SMAD4-independent pro-migratory signaling utilizing distinct mitogenic signaling pathways that affect EMT. p21 localization in colon cancer may determine a dominant activin versus TGFβ ligand signaling phenotype warranting further validation as a therapeutic biomarker prior to targeting TGFβ family receptors

Universality of three gaugino anomalous dimensions in N=4 SYM

We study maximal helicity three gaugino operators in N=4 Super Yang-Mills theory. We show that the lowest anomalous dimension of scaling operators with generic finite spin can be expressed in terms of the universal anomalous dimension appearing at twist-2. This statement is rigourously proved at three loops. The reason for this universality between sectors with different twist is the hidden psu(1|1) invariance of the su(2|1) subsector of the theory.Comment: 13 pages, JHEP styl

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

Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM

We propose a closed expression for the three loop anomalous dimension of a class of twist-3 operators built with gauge fields and covariant derivatives. To this aim, we solve the long-range Bethe Ansatz equations at finite spin and provide a consistent analytical formula obtained assuming maximal transcendentality violation as suggested by the known one-loop anomalous dimension. The final result reproduces the universal cusp anomalous dimension and obeys recursion relations inspired by the principle of reciprocity invariance.Comment: 20 pages, JHEP styl

Spin/disorder correlations and duality in the c=1/2 string

We use the method of discrete loop equations to calculate exact correlation functions of spin and disorder operators on the sphere and on the boundary of a disk in the $c = 1/2$ string, both in the Ising and dual Ising matrix model formulations. For both the Ising and dual Ising theories the results on the sphere are in agreement with the KPZ/DDK scaling predictions based on Liouville theory; the results on the disk agree with the scaling predictions of Martinec, Moore, and Seiberg for boundary operators. The calculation of Ising disorder correlations on the sphere requires the use of boundary variables introduced in [hep-th/9510199], which have no matrix model analog. A subtlety in the calculation on the disk arises because the expansions of the correlation functions have leading singular terms which are nonuniversal; we show that this issue may be resolved by using separate cosmological constants for each boundary domain. These results give evidence that the Kramers-Wannier duality symmetry of the $c = 1/2$ conformal field theory survives coupling to quantum gravity, implying a duality symmetry of the $c = 1/2$ string even in the presence of boundary operators.Comment: 19 pages, LaTeX; final publication versio

Geodesic Distance in Planar Graphs

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy.Comment: 38 pages, 8 figures, tex, harvmac, eps

Apparent diffusion coefficient by diffusion-weighted magnetic resonance imaging as a sole biomarker for staging and prognosis of gastric cancer

Objective: To investigate the role of apparent diffusion coefficient (ADC) from diffusion-weighted magnetic resonance imaging (DW-MRI) when applied to the 7th TNM classification in the staging and prognosis of gastric cancer (GC). Methods: Between October 2009 and May 2014, a total of 89 patients with non-metastatic, biopsy proven GC underwent 1.5T DW-MRI, and then treated with radical surgery. Tumor ADC was measured retrospectively and compared with final histology following the 7th TNM staging (local invasion, nodal involvement and according to the different groups — stage I, II and III). Kaplan-Meier curves were also generated. The follow-up period is updated to May 2016. Results: Median follow-up period was 33 months and 45/89 (51%) deaths from GC were observed. ADC was significantly different both for local invasion and nodal involvement (P<0.001). Considering final histology as the reference standard, a preoperative ADC cut-off of 1.80×10–3 mm2 /s could distinguish between stages I and II and an ADC value of ≤1.36×10–3 mm2 /s was associated with stage III (P<0.001). Kaplan-Meier curves demonstrated that the survival rates for the three prognostic groups were significantly different according to final histology and ADC cut-offs (P<0.001). Conclusions: ADC is different according to local invasion, nodal involvement and the 7th TNM stage groups for GC, representing a potential, additional prognostic biomarker. The addition of DW-MRI could aid in the staging and risk stratification of GC

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