Getting the D-brane effective action from BPS configurations

In this Ph.D. thesis, accepted at the Vrije Universiteit Brussel, we review and elaborate on a method to find the D‐brane effective action, based on BPS equations. Firstly, both for the Yang‐Mills action and the Born‐Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D‐brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in α′ four‐derivative corrections to the effective action and the BPS equations while in the non‐abelian case we obtained the effective action up to order α′4. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which would be the first step to use the method of Weyl invariance in N = 2 superspace in order to again construct the D‐brane effective action. A more detailed summary of each section can be found in the introduction.

Within Euclidean SU(2) Yang-Mills theory considered in certain constant non-Abelian background fields the explicit construction of gluon and ghost Green functions is presented, paying special attention to unstable modes. The propagators obtained turn out to be purely real. The propagator expressions given for two different background fields are related to each other in the coincidence limit of these background configurations. On the basis of the derived results the imaginary part of the Euclidean Yang-Mills theory effective action is discussed, showing that no higher-loop corrections beyond the well known 1-loop result appear. Also arguments are given that the 1-loop imaginary part should not be trusted.

In the early theoretical investigations [1–4] of the Integral Quantum Hall Effect (IQHE) [5,6], it was recognized that the observed plateaus of quantized Hall conductance should be explainable from the two-dimensional, free electron gas subject to a constant magnetic background field and to a random impurity potential. The concept of localization due to the randomness turned out to be essential in the explanation of the width of the plateaus, as well as the precision of the quantization [7].

Vector field effective action in the open superstring theory

We consider a D2-brane in the pp-wave backgrounds obtained from AdS$_4\times$CP$^3$ when electric and magnetic fields have been turned on. Upon fixing the light-cone gauge, light-cone Hamiltonian and BPS configurations are obtained. In particular we study BPS configurations with electric dipole on the two sphere giant and a giant graviton rotating in transverse directions. Moreover we show that the gauge field living on the D2-brane is replaced by a scalar field in the light-cone Hamiltonian. We also present a matrix model by regularizing (quantizing) 2-brane theory.

Understanding how a magnetic field affects the interaction of magnetic nanoparticles (MNPs) with cells is fundamental to any potential downstream applications of MNPs as gene and drug delivery vehicles. Here, we present a quantitative analysis of how a pulsed magnetic field influences the manner in which MNPs interact with and penetrate across a cell monolayer. Relative to a constant magnetic field, the rate of MNP uptake and transport across cell monolayers was enhanced by a pulsed magnetic field. MNP transport across cells was significantly inhibited at low temperature under both constant and pulsed magnetic field conditions, consistent with an active mechanism (i.e., endocytosis) mediating MNP transport. Microscopic observations and biochemical analysis indicated that, in a constant magnetic field, transport of MNPs across the cells was inhibited due to the formation of large (>2 μm) magnetically induced MNP aggregates, which exceeded the size of endocytic vesicles. Thus, a pulsed magnetic field enhances the cellular uptake and transport of MNPs across cell barriers relative to a constant magnetic field by promoting accumulation while minimizing magnetically induced MNP aggregation at the cell surface.

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

A constant magnetic field can significantly improve the quality and speed of ablation by nanosecond laser pulses. These improvements are usually attributed to the confinement of laser-produced plasma by the magnetic field and specific propagation effects in the magnetized plasma. Here we report a strong influence of constant axial magnetic field on the ablation of silicon by 20-ns laser pulses at wavelength 355 nm, which results in an increase of ablation depth by a factor of 1.3 to 69 depending on laser parameters and magnitude of the magnetic field. The traditional plasma effects do not explain this result, and magneto-absorption of silicon is proposed as one of the major mechanisms of the significant enhancement of ablation.

The study of the facts and circumstances of the unaccounted use of energy resources by consumers, primarily electric energy, natural gas, hot and cold water in the practice of conducting electrical and heat engineering types of forensic examinations, is one of the most common. The initial data in forensic research in this area, namely the data of acts on the violation of the consumption of these energy resources, including information on fixing the impact on the metering device of a constant magnetic field by magnetic field effect indicator (MFEI), which in the cases under study is usually denied by the consumer as his intentional actions to create such a field. The expert task of forensic examinations in this area requires an unambiguous definition of the operation of a MFEI from a constant magnetic field with certain power characteristics, with the exclusion of other factors of influence. The most common modern designs of magnetic field impact indicators in use, which are installed by energy sales enterprises as fixing technical means of interfering with the operation of consumer metering devices when using energy resources as a result of exposure to an external constant magnetic field, are considered. The triggering mechanism of MFEI of different designs is analyzed. According to the constructive construction and principle of operation, the indicators of the influence of the magnetic field are divided into separate classification groups. Signs of atypical triggering of the MFEI are considered. Cases of activation of indicators of the impact of the magnetic field are determined, requiring a comprehensive study using research methods of various forensic specialties to establish the fact of interference in the operation of metering devices in order to unaccounted for the consumption of energy resources. Recommendations are given on the application of the method of modeling a constant magnetic field with the reproduction of the conditions for the operation of the investigated MFEI to establish the fact of interference in the operation of the meter by exposing it to an external constant magnetic field in order to unaccounted for the consumption of energy resources. The necessity of performing a check of the operable state of the MFEI in expert experience in the study of the fact of the existence of the influence of a constant magnetic field on the metering device for energy consumption is substantiated.

We present a short review of how the effective action formalism, well known in relativistic quantum field theory, can be used to discuss Bose-Einstein condensation of non-relativistic gases. This method lends itself very naturally to an interpretation of Bose-Einstein condensation in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalized ζ-functions. We show how this method can be used to recover the well known results for the free boson gas, as well as the charged boson gas in a constant magnetic field. A general criterion for interpreting Bose-Einstein condensation in terms of a phase transition with symmetry breaking is given. Finally we present an analysis of Bose-Einstein condensation in a harmonic oscillator confining potential trap, and show how the results of this simple model are in excellent agreement with experiment.

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a suitable representation. The relativistic symmetry associated with the magnetic field is carefully respected. Considering eigenstates of the pseudo momentum four-vector, we separate out collective variables and obtain a 3- dimensional reduced equation, posing a nonconventional eigenvalue problem. The velocity of the system as a whole generates "motional" terms in the formulas these terms are taken into account within a manifestly covariant framework.

To investigate the effects of constant magnetic field (CMF) on proliferation and migration of bone marrow-derived endothelial progenitor cells (EPCs) under rapamycin intervention. EPCs were isolated from rat bone marrow by density gradient centrifugation and cultured on fibronectin-coated dishes. Six days later the attached cells were divided into 5 groups: control group, rapamycin (1 ng/ml) group, and 3 rapamycin + CMF groups (treated with CMF of the doses 0.1 mT, 0.5 mT, and 1.0 mT respectively). Samples were collected 24 hours after incubation. Cell proliferation was measured by MTT chromatometre. EPC migration was detected with modified Boyden chamber assay. The EPC proliferation ability of the rapamycin group, expressed by absorbance, was (0.252 +/- 0.006), significantly lower than that of the control group [(0.328 +/- 0.025), P < 0.05]. The number of migrating EPC was (31 +/- 3) cells, significantly lower than that of the control group [(48 +/- 5), P < 0.05]. The EPC proliferation ability of the rapamycin + CMF 0.5 mT and 1.0 mT groups, expressed by absorbance, were (0.278 +/- 0.008) and (0.280 +/- 0.010) respectively, both significantly higher than that of the control group (both P < 0.05). The migrating EPC number of the rapamycin + CMF 0.5 mT and 1.0 mT groups were (37 +/- 3) and (38 +/- 4) respectively, both significantly higher than that of the control group (both P < 0.05). CMF of the doses of 0.5 mT and 1.0 mT antagonizes the effects of rapamycin on EPCs, increasing the proliferation and migration of EPCs.

In this contribution, we present our recent compact master formulas for the multiphoton amplitudes of a scalar propagator in a constant background field using the worldline fomulation of quantum field theory. The constant field has been included nonperturbatively, which is crucial for strong external fields. A possible application is the scattering of photons by electrons in a strong magnetic field, a process that has been a subject of great interest since the discovery of astrophysical objects like radio pulsars, which provide evidence that magnetic fields of the order of 1012G are present in nature. The presence of a strong external field leads to a strong deviation from the classical scattering amplitudes. We explicitly work out the Compton scattering amplitude in a magnetic field, which is a process of potential relevance for astrophysics. Our final result is compact and suitable for numerical integration.

1. The impulse activity of single nerve fibers supplying the ampullae of Lorenzini in hyoid group of the Black Sea skate, was recorded to study the response of these receptors to various modifications of stimulation with the vertical component of a magnetic field. 2. When the animal was at rest in motionless water an impulse reaction was observed only with changes in magnetic field, a constant field had no effect. The intensity of response was determined by the rate of magnetic field change (dB/dt). 3. The nature of responses to magnetic field changes depended on the orientation of the ampullary canals relative to induced currents in the animal's body and in the surrounding sea water (Figs. 1, 2 and 3). 4. The intensity of response of a single receptor to magnetic field changes decreased with the shortening of the ampullary canal under study (Fig. 4); cutting of the other canals or dissection of the capsule of the ampullary cluster appeared to have no effect. 5. The receptors of the ampullae of Lorenzini were shown to respond to a constant magnetic field when the fish moved in water, or when water was moved with respect to the fish (Figs. 5 and 6). 6. The character of impulse responses to a constant magnetic field depended on the direction of the field and the direction of movement of either the fish or the water. The relationship between the response intensity and magnetic field, or velocity of water flow is roughly linear (Figs. 7 and 8). 7. Symmetrical receptors on the right and left sides of the animal's body responded oppositely to stimulation by either increasing or constant magnetic field (Figs. 1 and 6). 8. Experiments involving compensation for the Earth's magnetic field with Helmholtz coils revealed a statistically significant reaction to the vertical component of the geomagnetic field (0.35 Gs in the region of the Karadag Biological Station, the Crimea). 9. The mechanisms and functional role of the detection of changing and constant magnetic field by the ampullae of Lorenzini are discussed.