Algebraic Curve for a Cusped Wilson Line

We consider the classical limit of the recently obtained exact result for the anomalous dimension of a cusped Wilson line with the insertion of an operator with L units of R-charge at the cusp in planar N=4 SYM. The classical limit requires taking both the 't Hooft coupling and L to infinity. Since the formula for the cusp anomalous dimension involves determinants of size proportional to L, the classical limit requires a matrix model reformulation of the result. We construct such matrix model-like representation and find corresponding classical algebraic curve. Using this we derive the classical value of the cusp anomalous dimension and the 1-loop correction to it. We check our results against the energy of the classical solution and numerically by extrapolating from the quantum regime of finite L.Comment: 15 pages, 2 figure

Skaitmeninio dvynio koncepcinė analizė

Skaitmeniniai dvyniai yra naudojami labai įvairiose tiek mokslo, tiek pramonės srityse ir reiškia objektų, sistemų ar procesų virtualių kopijų kūrimą. Tačiau nėra vieningos skaitmeninio dvynio sampratos. Mokslinėje literatūroje skaitmeniniais dvyniais vadinamas platus modelių spektras – nuo naudotojo profilio iki realios esybės išsamaus vykdomo analogo. Šio darbo tikslas yra atlikus sistemingą literatūros analizę atsakyti į klausimą „Kokias būtinas savybes turi turėti esybės modelis, kad jį būtų galima pavadinti skaitmeniniu dvyniu?“. Atsakant į tyrimo klausimą sudarytas skaitmeninio dvynio metasavybių rinkinys, kuris nusako minimalią savybių grupę, kai skaitmeninis dvynys yra suprantamas kaip virtuali realios esybės kopija

Exact Results in Supersymmetric Gauge Theories

In this thesis we discuss supersymmetric gauge theories, focusing on exact results achieved using methods of integrability. For the larger portion of the thesis we study the N=4 super Yang-Mills theory in the planar limit, a recurring topic being the Konishi anomalous dimension, which is roughly the analogue for the mass of the proton in quantum chromodynamics. The N=4 supersymmetric Yang-Mills theory is known to be integrable in the planar limit, which opens up a wealth of techniques one can employ in order to find results in this limit valid at any value of the coupling. We begin with perturbation theory where the integrability of the theory first manifests itself. Here we showcase the first exact result, the so-called slope function, which is the linear small spin expansion coefficient of the generalized Konishi anomalous dimension. We then move on to exact results mainly achieved using the novel quantum spectral curve approach, the method allowing one to find scaling dimensions of operators at arbitrary values of the coupling. As an example we find the second coefficient in the small spin expansion after the slope, which we call the curvature function. This allows us to extract non-trivial information about the Konishi operator. Methods of integrability are also applicable to other supersymmetric gauge theories such as ABJM, which in fact shares many similarities with N=4 super Yang-Mills. We briefly review these parallel developments in the last chapter of the thesis.Comment: PhD thesis, 154 page

In Our Defense : Sheridan\u27s The Camp, The Glorious First of June, Pizarro and The Fate of the British Nation in Late Eighteenth-Century England

In this thesis, I examine Richard Brinsley Sheridan’s plays The Camp (1778), and The Glorious First o f June (1794), and Pizarro (1799), and how they dealt with the British invasion crisis of the late eighteenth and early nineteenth centuries. I investigate how Sheridan’s theatrical works confronted and presented British fears of national/racial annihilation and in turn how society used these plays to understand them. In particular, I want to consider the ways Sheridan’s works attempted to influence the audience members’ feelings about participating in the military to defend the British nation. Although Sheridan’s play Pizarro is often examined in regards to how British national identity shaped ideas surrounding British colonial activities as well as the invasion crisis, I take a broader look at Sheridan’s works and the ways they dealt with the interactions of national identity, class, and gender within the defense of the British nation during this period.). I argue that, for Sheridan, the problem of who was left to defend the British nation was ultimately an issue of the lack of male members of the middle-class taking part in the military in a defensive capacity in Great Britain. Sheridan’s military plays are marked by their problematic portrayal of middle-class characters who involved in the fight to defend their homeland; despite the level of class-consciousness in the plays there is a dearth of middle-class characters over all. The ones that are present are marked by corruption and greed, and more often than not problematize national defense rather than support it. Sheridan’s plays call for increased, active male middle-class participation in the defense of the British nation at a time in which the primary concern of the nation, regardless of class or political affiliation, was its military defense. Sheridan’s choice to use theatrical performance along with his political position to achieve these goals shows the power and dexterity of the stage to influence public opinion and even an audience’s ways of identifying and understanding its own national and racial selfhood

Semiclassical folded string in AdS4 X CP3

We consider type IIA superstring theory on the background AdS4 x CP3, and the classical solution describing a folded string spinning in AdS4 with angular momentum in CP3. In the 't Hooft limit, it is the gravity dual of twist operators in the ABJM superconformal theory. We quantize the classical solution by algebraic curve methods and determine the first semiclassical correction to the energy. We provide an integral representation for this quantity valid for all values of the charges. We analyze its properties in the special regimes associated with a short or long string providing various accurate analytical expansions. Finally, we investigate various properties of the so-called slope, the leading term of the energy for short strings, collecting information that could be useful in attempts to generalize the exact results recently proposed for the folded string in AdS5 x S5.Comment: 23 pages, 1 pdf figure, JHEP style, typo correcte

An interdisciplinary learning approach to ecological business: Using examples of best practice

It is a widely held view among educationists that the most effective way to facilitate a holistic learning approach is to present visual, ready-to-use, practical examples. Thus, our study follows the general scope of the course “Socially responsible ecological business”, which is currently offered to master students at the Vilnius Gediminas Technical University (VGTU). We contend that teaching materials should be presented visually using case studies and examples. Indeed, simple guidance is one of the vital learning tools for students. Accordingly, and in line with the aims of the course, the observations and experience of differences in global culture and our inclusion of a wide range of ecological examples were central to the design of our international case study. In particular, students found the case study on ecological business both useful and applicable in the real world

Экзистенциальное общение как основа подлинного человеческого существования в философии Карла Ясперса

The article analyzes from different aspects the conception of existential communication and its significance from the perspective of Karl Jaspers’s existential philosophy. An attempt is made to prove that the need for existential communication is primordial and naturally linked with human existence. On this basis, the definition of existential communication as life communication, is formed and analyzed. Ties between existential communication and existential truth are singled out

Large social inequalities and low levels of socio-economic segregation in Vilnius

The city of Vilnius has experienced major shifts in occupational structure between 2001 and 2011 and at the same time there were major transitions in the housing market and suburbanization. The main aim of this chapter is to get more insight in recent socio-economic segregation processes in Vilnius. We used occupational groups as a proxy for socio-economic status, and census tract level data to measure segregation in Vilnius and its three main housing zones during 2001 and 2011. Notwithstanding the major economic and social changes of post-communist society, we found low levels of segregation and modest change during the last decade. Local patterns of segregation were explored using location quotient maps. The analyses illustrated a deepening social divide in the city between the relatively rich north and the poorer south of the city, but the inner city changes are somehow ambiguous. In this chapter we argue that the main factors of socio-spatial change in Vilnius are related to an exceptionally high share of housing estates in the city and the polycentric urban system of the country. Together with 'fast-track' reforms after 1990 this urban system gave a unique character to the current processes and patterns of segregation