Modular Constraints on Superconformal Field Theories

We constrain the spectrum of $\mathcal{N}=(1, 1)$ and $\mathcal{N}=(2, 2)$ superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the $\Gamma_\theta$ congruence subgroup of the full modular group $SL(2, \mathbb{Z})$. We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without $U(1)$ charges. Especially, the upper bounds on the twist gap for the non-current primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to $\Gamma_\theta$. Some of the candidate theories have been discussed by H\"ohn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS$_3$.Comment: 50 pages, 16 figure

Modular Constraints on Conformal Field Theories with Currents

We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by $\mathcal{W}$-algebras of various type and observe that the bounds on the gap depend on the choice of $\mathcal{W}$-algebra in the small central charge region.Comment: 49 pages, 23 figure

A Design of MAC Model Based on the Separation of Duties and Data Coloring: DSDC-MAC

Among the access control methods for database security, there is Mandatory Access Control (MAC) model in which the security level is set to both the subject and the object to enhance the security control. Legacy MAC models have focused only on one thing, either confidentiality or integrity. Thus, it can cause collisions between security policies in supporting confidentiality and integrity simultaneously. In addition, they do not provide a granular security class policy of subjects and objects in terms of subjects\u27 roles or tasks. In this paper, we present the security policy of Bell_LaPadula Model (BLP) model and Biba model as one complemented policy. In addition, Duties Separation and Data Coloring (DSDC)-MAC model applying new data coloring security method is proposed to enable granular access control from the viewpoint of Segregation of Duty (SoD). The case study demonstrated that the proposed modeling work maintains the practicality through the design of Human Resources management System. The proposed model in this study is suitable for organizations like military forces or intelligence agencies where confidential information should be carefully handled. Furthermore, this model is expected to protect systems against malicious insiders and improve the confidentiality and integrity of data

Fabrication and tuning of plasmonic optical nanoantennas around droplet epitaxy quantum dots by cathodoluminescence

We use cathodoluminescence to locate droplet epitaxy quantum dots with a precision $\lesssim$ nm before fabricating nanoantennas in their vicinity by electron-beam lithography. Cathodoluminescence is further used to evidence the effect of the antennas as a function of their length on the light emitted by the dot. Experimental results are in good agreement with numerical simulations of the structures

Decay dynamics and exciton localization in large GaAs quantum dots grown by droplet epitaxy

We investigate the optical emission and decay dynamics of excitons confined in large strain-free GaAs quantum dots grown by droplet epitaxy. From time-resolved measurements combined with a theoretical model we show that droplet-epitaxy quantum dots have a quantum efficiency of about 75% and an oscillator strength between 8 and 10. The quantum dots are found to be fully described by a model for strongly-confined excitons, in contrast to the theoretical prediction that excitons in large quantum dots exhibit the so-called giant oscillator strength. We attribute these findings to localized ground-state excitons in potential minima created by material intermixing during growth. We provide further evidence for the strong-confinement regime of excitons by extracting the size of electron and hole wavefunctions from the phonon-broadened photoluminescence spectra. Furthermore, we explore the temperature dependence of the decay dynamics and, for some quantum dots, observe a pronounced reduction in the effective transition strength with temperature. We quantify and explain these effects as being an intrinsic property of large quantum dots owing to thermal excitation of the ground-state exciton. Our results provide a detailed understanding of the optical properties of large quantum dots in general, and of quantum dots grown by droplet epitaxy in particular.Comment: 13 pages, 7 figure