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

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

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

Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2 and D_2 on page 29 we corrected the rational part of the strong coupling predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table

Deeper Look into Short Strings

Using a recent conjecture of Basso we compute three leading nontrivial coefficients in the strong coupling expansion of the anomalous dimensions of short operators in the sl2 sector of AdS/CFT. We show that our results are consistent with the numerical results obtained using the Y-system and TBA approach earlier thus providing further support to the Y-system conjecture.Comment: v2: S^3 and S^4 orders are added in Sec.3.1 and App.B, minor misprints fixed v3: updated numerics sectio

Influence of CO2 on biomethane conversion parameters

Darbe pateikti sintezės dujų (H2 ir CO) gavimo optimalūs parametrai konvertuojant biometaną vandens garais ir vandens garų–deguonies mišiniais. Endoterminės konversijos metu optimaliomis sąlygomis (927 oC, 1–5 atm) sintezės dujų produktų santykis H2 / CO = 2 atitiktų biodujų sudėtį: ~64 % CH4, 32 % CO2, 4 % priemaišų. Egzoterminės konversijos atveju optimaliomis sąlygomis (1027–1127 oC, 1–20 atm) biodujų sudėtis būtų: ~80–82 % CH4, 13–15 % CO2, 5–6 % priemaišų. Eksperimentiškai nustatyta galimybė koreguoti CO2 koncentraciją biodujose vandeniniais metildietanolamino (MDEA) tirpalais ir pateikti proceso pusiausvirieji rodikliai. Absorbento prisotinimo laipsnis α labiau didėja 1 % koncentracijos MDEA tirpaluose nei 3 ir 5 % koncentracijos MDEA tirpaluose. Didėjant proceso temperatūrai nuo 21 iki 58 oC, 3 % MDEA tirpalu absorbuotas pusiausvirasis CO2 kiekis lėtai mažėjaThe aim of this work was to determine the optimal parameters of biomethane catalytic conversion to syngas and to estimate the possibility to regulate CO2 concentration in biogas by absorption using methyldiethanolamine (MDEA) aqueous solutions. A thermodynamic analysis showed that an efficient biogas conversion to syngas (the ratio H2 / CO = 2) could be carried out using endothermic or exothermic processes. In both cases, CO2 concentration should be diminished from 35% (raw biogas) to 32% (endothermic conversion) or 14% (exothermic conversion). This can be achieved by using 1–5% MDEA aqueous solutions. The absorption of CO2 with MDEA was studied experimentally and some operational parameters of CO2 removal were determined. For example, in order to decrease CO2 concentration from 35 to 32 or 14%, every 100 m3 of biogas should be in contact for ~10 min with 2.5–3.0 m3 or 17.0–17.5 m3 of 5% MDEA solution, respectively. By increaseing the temperature of the absorption process from 21 to 58 oC, the amount of chemisorbed CO2 is slightly decreased. On the basis of the obtained results, the mechanisms and technological peculiarities of biomethane conversion to syngas are discussedKauno technologijos universitetas, [email protected] technologijos universitetas, [email protected] technologijos universitetas, [email protected] technologijos universitetas, [email protected] Didžiojo universitetasŽemės ūkio akademij