Localization and Large N reduction on S^3 for the Planar and M-theory limit

We show a large N reduction on S^3 in a BPS sector for a broad class of theories : N>=2 supersymmetric Chern-Simons theory with any number of adjoint and bi-fundamental chiral multiplets.We show that a localization method can be applied to the reduced model and the path integral can be written by a multi-contour integral. By taking a particular localization configuration, we also show that the large N equivalence between the original theory on S^3 and the reduced model holds for the free energy and the expectation value of BPS Wilson loops. It turns out that the large N reduction on S^3 holds also for the M-theory limit.Comment: v1:39 pages, v2:40 pages, references added, typo fixe

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^{3/2} scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.Comment: 35 pages, 20 figures; reference added. The simulation code is available upon request to [email protected]

Conversion to complete resection with mFOLFOX6 with bevacizumab or cetuximab based on K‐RAS status for unresectable colorectal liver metastasis (BECK study): Long‐term results of survival

[Background/Purpose]To investigate the long‐term outcome and entire treatment course of patients with technically unresectable CRLM who underwent conversion hepatectomy and to examine factors associated with conversion to hepatectomy. [Methods]Recurrence and survival data with long‐term follow‐up were analyzed in the cohort of a multi‐institutional phase II trial for technically unresectable colorectal liver metastases (the BECK study). [Results]A total of 22/12 patients with K‐RAS wild‐type/mutant tumors were treated with mFOLFOX6 + cetuximab/bevacizumab. The conversion R0/1 hepatectomy rate was significantly higher in left‐sided primary tumors than in right‐sided tumors (75.0% vs 30.0%, P = .022). The median follow‐up was 72.6 months. The 5‐year overall survival (OS) rate in the entire cohort was 48.1%. In patients who underwent R0/1 hepatectomy (n = 21), the 5‐year RFS rate and OS rate were 19.1% and 66.3%, respectively. At the final follow‐up, seven patients had no evidence of disease, five were alive with disease, and 20 had died from their original cancer. All 16 patients who achieved 5‐year survival underwent conversion hepatectomy, and 11 of them underwent further resection for other recurrences (median: 2, range: 1‐4). [Conclusions]Conversion hepatectomy achieved a similar long‐term survival to the results of previous studies in initially resectable patients, although many of them experienced several post‐hepatectomy recurrences. Left‐sided primary was found to be the predictor for conversion hepatectomy