Holography of Wrapped M5-branes and Chern-Simons theory

We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N^3 scaling with precise coefficients.Comment: 5 pages, 2 figures. Some clarifications, references added, misprint correcte

Holography of 3d-3d correspondence at Large N

We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an $\mathcal{N}=2$ superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS$_4$ geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspondence, we propose a conjecture for the large $N$ limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same $N^3$ scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large $N$. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the suppression of higher loop terms in a few examples.Comment: 37 pages, 7 figure

Developing Methods of Processing and Analyzing Genetic Data to Examine Tiger Salamander Population Structure

Professor Heather Waye and her colleagues conducted a pilot study in 2014 to measure genetic diversity and dispersal pattern in a population of tiger salamanders in west-central Minnesota. The ultimate goal of this research was to analyze the genetic differences between tiger salamander larvae captured in breeding ponds within Pepperton Waterfowl Production Area to understand the population structure and movement patterns. They expected that ponds closer to each other would have more similar genetic information, and that genetic differences between ponds would increase with geographic distance. However, the initial analysis using standard techniques failed to uncover useful patterns in the data. Reorganization of the data and other quantitative approaches are needed to discover any significant patterns in this sample. In my research, I attempted a different modeling method to determine whether re-manipulating samples will uncover hidden patterns of genetic variation. In order to investigate this process, I learned how to install and utilize a software pipeline called Stacks which uses a standard UNIX- like environment operating system called Ubuntu. This software pipeline is a new methodological approach that we are using to build ‘loci’, fixed positions of genetic markers on chromosomes, from short-read sequences to map the relationship between individual tiger salamanders. We hope this technique that interrogates DNA fragments will provide the potential genetic differences between individuals in the sample. My results improve understanding of how to use advanced statistical and computational methods tailored to complex problems with real-world data.https://digitalcommons.morris.umn.edu/urs_2018/1007/thumbnail.jp

Aspects of Defects in 3d-3d Correspondence

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group $SL(N, \mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theory $T_{N}[M]$. We establish a dictionary for this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, in particular for non-maximal punctures and $N>2$. We also highlight the non-Abelian description of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its Higgsing prescription and the resulting `refinement' in complex CS theory. This paper is a companion to our shorter paper arXiv:1510.03884, which summarizes our main results.Comment: 129 pages (sorry), 22 figure

Refined test of AdS4/CFT3 correspondence for N=2,3 theories

We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111}, M^{32} with N=2,3 supersymmetries and compare them with the corresponding dual gravity indices. For N^{010}, we find perfect agreements. In addition, for N^{010}/Z_k, we also find an agreement with the gravity index including the contributions from two types of D6-branes wrapping RP^3. For Q^{111}, we find that the model obtained by adding fundamental flavors to the N=6 theory has the right structure to be the correct model. For M^{32}, we find the matching with the gravity index modulo contributions from peculiar saddle points.Comment: 35 pages, 1 figure, v2: added references and comment

Saliency difference based objective evaluation method for a superimposed screen of the HUD with various background

The head-up display (HUD) is an emerging device which can project information on a transparent screen. The HUD has been used in airplanes and vehicles, and it is usually placed in front of the operator's view. In the case of the vehicle, the driver can see not only various information on the HUD but also the backgrounds (driving environment) through the HUD. However, the projected information on the HUD may interfere with the colors in the background because the HUD is transparent. For example, a red message on the HUD will be less noticeable when there is an overlap between it and the red brake light from the front vehicle. As the first step to solve this issue, how to evaluate the mutual interference between the information on the HUD and backgrounds is important. Therefore, this paper proposes a method to evaluate the mutual interference based on saliency. It can be evaluated by comparing the HUD part cut from a saliency map of a measured image with the HUD image.Comment: 10 pages, 5 fighres, 1 table, accepted by IFAC-HMS 201