Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory

In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by the generators of the Lie 3-algebra. The gauge and supersymmetry variations of the boundary theory will exactly cancel the boundary terms generated by the gauge and supersymmetric variations of the bulk theory.Comment: 15 pages, 0 figures, accepted for publication in JHE

Robust Structured Low-Rank Approximation on the Grassmannian

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the $\ell_p$-norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and real-world data

Boundary Conditions for Interacting Membranes

We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.Comment: 36 pages, latex, v2 minor typos correcte

Increased expression of cyclooxygenase-2 in first-degree relatives of gastric cancer patients

Aim: To study the expression of cyclooxygenase-2 (COX-2) in human gastric cancer tissues and their paired adjacent mucosa, as well as mucosa from gastric antrum and corpus of the first-degree relatives of the recruited cancer patients. Methods: The expression of COX-2 mRNA in 38 patients with gastric cancer and their 29 first-degree relatives and 18 healthy controls was assessed by the real time RT-PCR. The expression of COX-2 protein was determined by Western blot. Results: A marked increase in COX-2 mRNA expression was found in 20 of 37 (54%) cancerous tissues compared to their respective paired normal mucosa (P<0.001). Interestingly, increased COX-2 mRNA expression was also found in mucosa of the corpus (6/29) and antrum (13/29) of their first-degree relatives. Increased COX-2 mRNA expression was more frequently observed in the antrum biopsies from cancer patients than in the antrum biopsies from healthy controls (P<0.05). In addition, 3 of 23 (13%) patients with atrophic mucosa and 6 of 35 (17%) patients with intestinal metaplasia showed increased COX-2 mRNA expression. Furthermore, COX-2 expression increased in H pylori-positive tissues, especially in antrum mucosa. Conclusion: Increased COX-2 expression is involved in gastric carcinogenesis, and may be necessary for maintenance of the malignant phenotype and contribute to Helicobacter pylori-associated malignant transformation. © 2005 The WJG Press and Elsevier Inc. All rights reserved.published_or_final_versio

The Conformal Anomaly of M5-Branes

We show that the conformal anomaly for N M5-branes grows like $N^3$. The method we employ relates Coulomb branch interactions in six dimensions to interactions in four dimensions using supersymmetry. This leads to a relation between the six-dimensional conformal anomaly and the conformal anomaly of N=4 Yang-Mills. Along the way, we determine the structure of the four derivative interactions for the toroidally compactified (2,0) theory, while encountering interesting novelties in the structure of the six derivative interactions.Comment: 38 pages, LaTeX; references adde

Nonabelian (2,0) Tensor Multiplets and 3-algebras

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional gauge theory along with six-dimensional abelian (2,0) tensor multiplets. We briefly discuss possible applications to D4-branes using a spacelike reduction and M5-branes using a null reduction.Comment: 17 pages, Latex; v2: Typos corrected and references adde

Conformal field theories in anti-de Sitter space

In this paper we discuss the dynamics of conformal field theories on anti-de Sitter space, focussing on the special case of the N=4 supersymmetric Yang-Mills theory on AdS_4. We argue that the choice of boundary conditions, in particular for the gauge field, has a large effect on the dynamics. For example, for weak coupling, one of two natural choices of boundary conditions for the gauge field leads to a large N deconfinement phase transition as a function of the temperature, while the other does not. For boundary conditions that preserve supersymmetry, the strong coupling dynamics can be analyzed using S-duality (relevant for g_{YM} >> 1), utilizing results of Gaiotto and Witten, as well as by using the AdS/CFT correspondence (relevant for large N and large 't Hooft coupling). We argue that some very specific choices of boundary conditions lead to a simple dual gravitational description for this theory, while for most choices the gravitational dual is not known. In the cases where the gravitational dual is known, we discuss the phase structure at large 't Hooft coupling.Comment: 57 pages, 1 figure. v2: fixed typo

More on the Nambu-Poisson M5-brane Theory: Scaling limit, background independence and an all order solution to the Seiberg-Witten map

We continue our investigation on the Nambu-Poisson description of M5-brane in a large constant C-field background (NP M5-brane theory) constructed in Refs.[1, 2]. In this paper, the low energy limit where the NP M5-brane theory is applicable is clarified. The background independence of the NP M5-brane theory is made manifest using the variables in the BLG model of multiple M2-branes. An all order solution to the Seiberg-Witten map is also constructed.Comment: expanded explanations, minor corrections and typos correcte

Discrete and Stereospecific Oligomers Prepared by Sequential and Alternating Single Unit Monomer Insertion

Natural biopolymers, such as DNA and proteins, have uniform microstructures with defined molecular weight, precise monomer sequence, and stereoregularity along the polymer main chain that affords them unique biological functions. To reproduce such structurally perfect polymers and understand the mechanism of specific functions through chemical approaches, researchers have proposed using synthetic polymers as an alternative due to their broad chemical diversity and relatively simple manipulation. Herein, we report a new methodology to prepare sequence-controlled and stereospecific oligomers using alternating radical chain growth and sequential photoinduced RAFT single unit monomer insertion (photo-RAFT SUMI). Two families of cyclic monomers, the indenes and the N-substituted maleimides, can be alternatively inserted into RAFT agents, one unit at a time, allowing the monomer sequence to be controlled through sequential and alternating monomer addition. Importantly, the stereochemistry of cyclic monomer insertion into the RAFT agents is found to be trans-selective along the main chains due to steric hindrance from the repeating monomer units. All investigated cyclic monomers provide such trans-selectivity, but analogous acyclic monomers give a mixed cis- and trans-insertion