Indices for Superconformal Field Theories in 3,5 and 6 Dimensions

We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.Comment: a small typo corrected, 46 page

Supersymmetric States in Large N Chern-Simons-Matter Theories

In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter.Comment: 53 pages, 18 figures. v2: improved numerics, additional comments adde

Closed String Tachyon Condensation on Twisted Circles

We study IIA/B string theory compactified on twisted circles. These models possess closed string tachyons and reduce to type 0B/A theory in a special limit. Using methods of gauged linear sigma models and mirror symmetry we construct a conformal field theory which interpolates between these models and flat space via an auxiliary Liouville direction. Interpreting motion in the Liouville direction as renormalization group flow, we argue that the end point of tachyon condensation in all these models (including 0B/A theory) is supersymmetric type II theory. We also find a zero-slope limit of these models which is best described in a T-dual picture as a type II NS-NS fluxbrane. In this limit tachyon condensation is an interesting and well posed problem in supergravity. We explicitly determine the tachyon as a fluctuation of supergravity fields, and perform a rudimentary numerical analysis of the relevant flows.Comment: 21 pages plus appendices (12 pages), harvmac, 1 fig, v2: minor changes and references added, v3: minor changes version published in JHE

An Index for 4 dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times$ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.Comment: harvmac 40+16 pages, v3: references and table of contents added, typos fixe

Detecting colorectal cancer using electrical impedance spectroscopy: an ex vivo feasibility study

Objective: Colorectal cancer is the fourth most common cancer worldwide, with a lifetime risk of around 20%. Current solutions do not allow clinicians to objectively assess tissue abnormality during endoscopy and perioperatively. A solution capable of objectively assessing samples in real time could greatly improve the treatment process. A solution that can be integrated in minimally invasive diagnostics and management strategies to provide real-time point-of-care information would be greatly transformative. Electrical impedance spectroscopy (EIS) may provide such a solution. In this paper, we present a feasibility study on using EIS in assessing colorectal tissue. Approach: We performed tetrapolar EIS using ZedScan on excised human colorectal tumour tissue and the matched normal colonic mucosa in 22 freshly resected specimens following elective surgery for colorectal cancer. Histopathological examination was used to confirm the final diagnosis. Statistical significance was assessed with Wilcoxon signed rank test. Main results: Tetrapolar EIS could discriminate cancer with statistically significant results when applying frequencies between 305 Hz – 625 kHz (p < 0.05). 300 Ω was set as the transfer impedance threshold to detect cancer. Thus, the area under the corresponding receiver operating characteristic curve for this threshold was 0.7105. Significance: This feasibility study demonstrates that impedance spectra changes in colorectal cancer tissue are detectable and may be statistically significant, suggesting that EIS has the potential to be the core technology in a novel non-invasive point of care test for detecting colorectal cancer. These results warrant further development and increasing the size of the study with a device specificity designed for colorectal cancer

Investigations of the Influence of Chlorine Contained Aromatic and Maleimide Compounds on the Structure of the Vulcanizates Net on the Base of Polyblend and the Creation Technology of Heat and Radiation Durable Materials

Abstract The structural parameters (mоlеculаr mаss, plasticity, number оf chains&apos; nеt and cross-linked molecules) of thermal vulcanizers on the basis of butadiene-nitrile rubber and polyvinyl chloride blends were studied by viscosity and sоl-gеl аnаlуsis methods. Аn alteration оf polаr groups content (-С≡N, С=О, С-Сl) and unsaturation оf thermal and thermal irradiated vulcanizers were investigated. According to alterations of residual deformation&apos;s accumulation, relaxation of tension and equilibrium modulus in air and in fuel, the properties оf elastomers were established at temperature (373-473K) and radiation (1000-2000 kGy) aging

Closed String Tachyon Condensation: An Overview

These notes are an expanded version of a review lecture on closed string tachyon condensation at the RTN workshop in Copenhagen in September 2003. We begin with a lightning review of open string tachyon condensation, and then proceed to review recent results on localized closed string tachyon condensation, focusing on two simple systems, C/Z_n orbifolds and twisted circle compactifications.Comment: harvmac, 59 pages; references adde