On Certain Divisibility Property of Polynomials

We review the definition of D-rings introduced by H. Gunji & D. L. MacQuillan. We provide an alternative characterization for such rings that allows us to give an elementary proof of that a ring of algebraic integers is a D-ring. Moreover, we give a characterization for D-rings that are also unique factorization domains to determine divisibility of polynomials using polynomial evaluations

Strong Subadditivity, Null Energy Condition and Charged Black Holes

Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area surfaces that determine the entanglement entropy for the boundary theory, can penetrate into this forbidden region only for certain choices for the mass and the charge functions in the background. This penetration is then perceived as the violation of SSA in the boundary theory. We also find that this happens only when the critical surface lies above the apparent horizon, but not otherwise. We conjecture that SSA, which is thus non-trivially related to NEC, also characterizes the entire time-evolution process along which the dual field theory may thermalize.Comment: 27 pages, v3 matches the published versio

Weak Field Collapse in AdS: Introducing a Charge Density

We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large $N_c$ gauge theory in $(2+1)$-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis.Comment: 1+48 pages, multiple figures, published in JHE

The Exceptional Case of Plancia Magna: (Re)analyzing the Role of a Roman Benefactress

This thesis analyzes the extravagant renovation of the Hellenistic gate complex funded by Plancia Magna, an elite woman from Perge, a city in the Roman province of Pamphylia. By using Plancia Magna as a case study, I hope to use her patronage of an outstanding architectural program to examine the dynamic roles elite women held under the Roman Empire in the late 1st century to 2nd century CE. Euergetism played a key role in developing cultural standards and civic obligations. Predominantly a male dominated practice, Plancia Magna stands out as one of its active and independent participants by commissioning the costly renovation of her city’s gate complex. Elite city members participated in euergetism in order to promote themselves by bestowing benefactions that would not only benefit their city, but also legitimize their social standing, family, and wealth. These costly endeavors ranged from costly architectural programs such as nyphaeums and theaters, to providing resources such as oil and food to their fellow citizens. In the past, scholars, such as Sencer Sahin, Mary Boatwright, and Riet Van Bremen, focused on Plancia Magna’s familial ties in order to explain the few and unparalleled male references in the epigraphic evidence found in the gate complex. For example, while Plancia Magna included her father and brother in the statuary, they were uniquely identified by their connection to Plancia Magna. These scholars also focused on the absence of her husband or son by vigorously searching for any evidence that would essentially explain why she would decide not include them, rather than considering that she could have chosen to identify herself independently. Despite their efforts to provide a coherent historical timeline by analyzing the Plancii and Cornuti family, the two most prominent families of Perge, their work resulted in a forced analysis to justify her decisions behind the gate complex’s architectural, sculptural, and epigraphic program. This study is an attempt to first provide a historical and cultural context of Asia Minor, in order to provide a backdrop for Perge throughout its political transitions from Alexander’s death, the Hellenistic dynasts, and ultimately to the Roman Empire. After understanding the political and cultural developments that shaped Perge, I delve into a detailed analysis of the Hellenistic Gate complex, which was renovated under the patronage of Plancia Magna. By analyzing her architectural, sculptural, and epigraphic choices, Plancia Magna’s position within Perge, and the Roman East, could be reasserted through her individuality and independence

Spatial mapping of splicing factor complexes involved in exon and intron definition

We have analyzed the interaction between serine/arginine-rich (SR) proteins and splicing components that recognize either the 5′ or 3′ splice site. Previously, these interactions have been extensively characterized biochemically and are critical for both intron and exon definition. We use fluorescence resonance energy transfer (FRET) microscopy to identify interactions of individual SR proteins with the U1 small nuclear ribonucleoprotein (snRNP)–associated 70-kD protein (U1 70K) and with the small subunit of the U2 snRNP auxiliary factor (U2AF35) in live-cell nuclei. We find that these interactions occur in the presence of RNA polymerase II inhibitors, demonstrating that they are not exclusively cotranscriptional. Using FRET imaging by means of fluorescence lifetime imaging microscopy (FLIM), we map these interactions to specific sites in the nucleus. The FLIM data also reveal a previously unknown interaction between HCC1, a factor related to U2AF65, with both subunits of U2AF. Spatial mapping using FLIM-FRET reveals differences in splicing factors interactions within complexes located in separate subnuclear domains

Gravity duals of 2d supersymmetric gauge theories

We find new supergravity solutions generated by D5-branes wrapping a four-cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N=(2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G_2-holonomy, which provides a gravity dual of N=(1,1) supersymmetric Yang-Mills theory in two dimensions. We also discuss the addition of unquenched fundamental matter fields to these backgrounds and find the corresponding gravity solutions with flavor brane sources.Comment: 34 pages + appendices; v2: minor improvement

New Supergravity Backgrounds Dual to N=1 SQCD-like Theories with N_f=2N_c

We present new supergravity backgrounds generated by N_c D5-branes, wrapping the S^2 of the resolved conifold, in the presence of N_f = 2 N_c smeared flavor D5-branes. The smearing allows us to take their backreaction on the geometry into account. We discuss the consistency, stability, and supersymmetry of these types of setups. We find near horizon geometries that we expect to be supergravity duals of SQCD-like theories with N_f= 2N_c. From these backgrounds we numerically extract rectangular Wilson loops and beta functions of the dual field theory for the regime where our approximations are valid.Comment: 22+24 pages, 17 figures, Figure 12 replace