ShantanuT01/DACTYL-Pretraining huggingface dataset:
This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as mechanical models, evolving in one spacetime direction. This evolution parameter represents the orthogonal coordinate to the homogeneous foliation of the spacetime. I investigate their classical symmetries and the algebra of the corresponding Noether charges. After presenting the formalism allowing us to describe the reduced models in terms of an action principle, we discuss the condition for having an (extended) conformal symmetry. In particular, the black hole model enlightens the subtle role of the spacelike boundary of the homogeneous slice. The latter interplays with the conformal symmetry, being associated with a conserved quantity from the mechanical point of view. The absence of the infinite tower of charges, characteristic of the full theory, is due here to a symmetry-breaking mechanism. This is made explicit by looking at the infinite-dimensional extension of the symmetry group. This allows to look at the equation of motion of the mechanical system in terms of the infinite-dimensional group, who in turn has the effect of rescaling the coupling constants of the theory. Finally, the presence of the finite symmetry group allows defining a quantum model in terms of the corresponding representation theory. At the level of the effective theory, accounting for the quantum effects, the request that the symmetry is protected provides a powerful tool to discriminate between different modifications. In the end, the conformal invariance of the black hole background opens the door to its holographic properties and might have important consequences in the corresponding perturbation theory.
In this talk, I discuss theoretical advances in understanding the properties of the Higgs boson and the implications for models of electroweak symmetry breaking. I begin by reviewing some of the recent progress in Standard Model calculations for Higgs boson production and decay rates, followed by a lightning tour of the use of effective field theories in the search for new physics in the Higgs sector. I end with a discussion of the complementarity of precision Higgs coupling measurements and direct searches for heavy particles for the discovery of Beyond the Standard Model physics in the electroweak sector.
The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with ionization fraction $f$ as low as $10^{-4}$. In galactic star forming regions, $f$ can be $10^{-10}$ or lower. Under these circumstances, the Hall current can couple low frequency Alfv\'en and magneto\-acoustic waves via the dimensionless Hall parameter $\epsilon=\omega/\Omega_\text{i}f$, where $\omega$ is the wave frequency and $\Omega_\text{i}$ is the mean ion gyrofrequency. This is analysed in the context of a cold (zero-$\beta$) plasma, and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wave vector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfv\'en modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, $\epsilon$ is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star forming gas clouds suggest that $\mathcal{O}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfv\'en speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal L\'evy walks rather than Gaussian random walks with perturbations.
The thermodynamics and dynamics of a one dimensional dimer-forming anharmonic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat, correlation length, and order parameter are calculated three ways: (a) by mean field approximation, (b) by numerical molecular dynamics simulation, and (c) by an exact transfer matrix method. The single-particle spectrum (velocity-velocity correlation function) is found numerically and in mean field theory.
We show how to estimate the enclosed mass from the observed motions of an ensemble of test particles. Traditionally, this problem has been attacked through virial or projected mass estimators. Here, we examine and extend these systematically, and show how to construct an optimal estimator for any given assumption as to the potential. The estimators do not explicitly depend on any properties of the density of the test objects, which is desirable as in practice such information is dominated by selection effects. As particular examples, we also develop estimators tailored for the problem of estimating the mass of the Hernquist or NFW dark matter haloes from the projected positions and velocities of stars.
Let p be an odd prime, n an odd positive integer and C the p-Sylow subgroup the class group of the p-cyclotomic extension of the rationals. When log(p) is bigger than n**(224n**4), we prove that the eigenspace on C attached to the (p-n)-th power of the Teichmuller character is trivial. The proof uses the K-theory of the integers and the Voronoi reduction theory of quadratic forms.
Within the framework of the modified potential cluster model with the state classification of nuclear particles according to Young tableaux the possibility of describing the available experimental data for the total cross sections of the neutron radiative capture on 8Li at thermal and astrophysical energies was considered.
Given any two rational numbers $r_1$ and $r_2$, a necessary and sufficient condition is established for the three numbers $1$, $\cos (\pi r_1)$, and $\cos (\pi r_2)$ to be rationally independent. Extending a classical fact sometimes attributed to I. Niven, the result even yields linear independence over larger number fields. The tools employed in the proof are applicable also in the case of more than two trigonometric numbers. As an application, a complete classification is given of all planar triangles with rational angles and side lengths each containing at most one square root. Such a classification was hitherto known only in the special case of right triangles.
We examine how to construct explicit heterotic string models dual to F-theory in eight dimensions. In doing so we learn about where the moduli spaces of the two theories overlap, and how non-perturbative features leave traces on a purely perturbative level. We also propose a modified T-duality linking M and F-theories based on non-perturbative structures of string theories in eight dimensions.
We review the application of twist deformation formalism and the construction of noncommutative gauge theory on $\kappa$-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider ${U}(1)$ gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.
The peeling properties of a lightlike signal propagating through a general Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum space-time are studied. We demonstrate that in general the peeling behavior is the conventional one which is associated with a radiating isolated system and that it becomes unconventional if the asymptotically flat space-times on either side of the history of the light-like signal tend to flatness at future null infinity faster than the general Bondi-Sachs space-time. This latter situation occurs if, for example, the space-times in question are static Bondi-Sachs space- times.
Let $\mathcal{KC}_g ^k$ be the moduli stack of pairs $(S,C)$ with $S$ a $K3$ surface and $C\subset S$ a genus $g$ curve with divisibility $k$ in $\mathrm{Pic}(S)$. In this article we study the forgetful map $c_g^k:(S,C) \mapsto C$ from $\mathcal{KC}_g ^k$ to $\mathcal{M}_g$ for $k>1$. First we compute by geometric means the dimension of its general fibre. This turns out to be interesting only when $S$ is a complete intersection or a section of a Mukai variety. In the former case we find the existence of interesting Fano varieties extending $C$ in its canonical embedding. In the latter case this is related to delicate modular properties of the Mukai varieties. Next we investigate whether $c_g^k$ dominates the locus in $\mathcal{M}_g$ of $k$-spin curves with the appropriate number of independent sections. We are able to do this only when $S$ is a complete intersection, and obtain in these cases some classification results for spin curves.
We investigate the effect induced by variations in the density profile of the Earth's interior using a long-baseline neutrino oscillation experiment.   At first, we point out two facts. (i) The most essential part of the matter profile is the first Fourier mode of the matter profile function; and (ii) The Earth models based on the study of seismology include a large uncertainty for the first Fourier mode.   Next, we show that there is a strong correlation between the average density value and the first Fourier coefficient in the analysis of oscillation probability.   This means that the matter profile effect induces added uncertainty for the average matter parameter. %although the average density can be determined at a few percent accuracy.   Taking into account this extra uncertainty, we make numerical calculations for the sensitivity to CP violation search and show that CP sensitivity is impaired by this added uncertainty within a large $U_{e3}$ region.
We present the first complete calculation of the history of the inhomogeneous 21-cm signal from neutral hydrogen during the era of the first stars. We use hybrid computational methods to capture the large-scale distribution of the first stars, whose radiation couples to the neutral hydrogen emission, and to evaluate the 21-cm signal from z ~ 15-35. In our realistic picture large-scale fluctuations in the 21-cm signal are sourced by the inhomogeneous density field and by the Ly-alpha and X-ray radiative backgrounds. The star formation is suppressed by two spatially varying effects: negative feedback provided by the Lyman-Werner radiative background, and supersonic relative velocities between the gas and dark matter. Our conclusions are quite promising: we find that the fluctuations imprinted by the inhomogeneous Ly-alpha background in the 21-cm signal at z ~ 25 should be detectable with the Square Kilometer Array.
Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment, or if the applied transformation is correlated with the state of the system. We provide a physically motivated definition of accessible non-CP maps and derive two necessary conditions for a map to be accessible. We also show that entanglement between the system and the environment is not necessary to generate a non-CP dynamics. We describe two simple approximations that may be sufficient for some problems in process tomography, and then outline what these methods may be able to tell us in other situations where non-CP dynamics naturally arise.
A gravitational wave event, S190510g, which was classified as a binary-neutron-star coalescence at the time of preliminary alert, was detected by LIGO/Virgo collaboration on May 10, 2019. At 1.7 hours after the issue of its preliminary alert, we started a target-of-opportunity imaging observation in Y-band to search for its optical counterpart using the Hyper Suprime-Cam (HSC) on the Subaru Telescope. The observation covers a 118.8 deg$^2$ sky area corresponding to 11.6% confidence in the localization skymap released in the preliminary alert and 1.2% in the updated skymap. We divided the observed area into two fields based on the availability of HSC reference images. For the fields with the HSC reference images, we applied an image subtraction technique; for the fields without the HSC reference images, we sought individual HSC images by matching a catalog of observed objects with the PS1 catalog. The search depth is 22.28 mag in the former method and the limit of search depth is 21.3 mag in the latter method. Subsequently, we performed visual inspection and obtained 83 candidates using the former method and 50 candidates using the latter method. Since we have only the 1-day photometric data, we evaluated probability to be located inside the 3D skymap by estimating their distances with photometry of associated extended objects. We found three candidates are likely located inside the 3D skymap and concluded they could be an counterpart of S190510g, while most of 133 candidates were likely to be supernovae because the number density of candidates was consistent with the expected number of supernova detections. By comparing our observational depth with a light curve model of such a kilonova reproducing AT2017gfo, we show that early-deep observations with the Subaru/HSC can capture the rising phase of blue component of kilonova at the estimated distance of S190510g (~230 Mpc).
Deep networks trained on millions of facial images are believed to be closely approaching human-level performance in face recognition. However, open world face recognition still remains a challenge. Although, 3D face recognition has an inherent edge over its 2D counterpart, it has not benefited from the recent developments in deep learning due to the unavailability of large training as well as large test datasets. Recognition accuracies have already saturated on existing 3D face datasets due to their small gallery sizes. Unlike 2D photographs, 3D facial scans cannot be sourced from the web causing a bottleneck in the development of deep 3D face recognition networks and datasets. In this backdrop, we propose a method for generating a large corpus of labeled 3D face identities and their multiple instances for training and a protocol for merging the most challenging existing 3D datasets for testing. We also propose the first deep CNN model designed specifically for 3D face recognition and trained on 3.1 Million 3D facial scans of 100K identities. Our test dataset comprises 1,853 identities with a single 3D scan in the gallery and another 31K scans as probes, which is several orders of magnitude larger than existing ones. Without fine tuning on this dataset, our network already outperforms state of the art face recognition by over 10%. We fine tune our network on the gallery set to perform end-to-end large scale 3D face recognition which further improves accuracy. Finally, we show the efficacy of our method for the open world face recognition problem.
Phosphorene, a single layer of black phosphorus, is a direct-band gap two-dimensional semiconductor with promising charge and spin transport properties. The electronic band structure of phosphorene is strongly affected by the structural anisotropy of the underlying crystal lattice. We describe the relevant conduction and valence bands close to the $\Gamma$ point by four- and six-band (with spin) $k \cdot p$ models, including the previously overlooked interband spin-orbit coupling which is essential for studying anisotropic crystals. All the $k \cdot p$ parameters are obtained by a robust fit to {\it ab initio} data, by taking into account the nominal band structure and the $k$-dependence of the effective mass close to $\Gamma$-point. The inclusion of interband spin-orbit coupling allows us to determine dipole transitions along both armchair and zigzag directions. The interband coupling is also key to determine the effective g-factors and Zeeman splittings of the Landau levels. We predict the electron and hole g-factor correction of $\approx 0.03$ due to the intrinsic contributions in phosphorene, which lies within the existing range of experimental data. Furthermore, we investigate excitonic effects using the $k \cdot p$ models and find exciton binding energy (0.81 eV) and exciton diameters consistent with experiments and {\it ab initio} based calculations. The proposed $k \cdot p$ Hamiltonians should be useful for investigating magnetic, spin, transport, optical properties and many-body effects in phosphorene.
Structural phase transitions between semiconductors and topological insulators have rich applications in nanoelectronics but are rarely found in two-dimensional (2D) materials. In this work, by combining ab initio computations and evolutionary structure search, we investigate two stable 2D forms of gold(I) telluride (Au$_{2}$Te) with square symmetry, noted as s(I)- and s(II)-Au$_{2}$Te. s(II)-Au$_{2}$Te is the global minimum structure and is a room-temperature topological insulator. s(I)-Au$_{2}$Te is a direct-gap semiconductor with high carrier mobilities and unusual in-plane negative Poisson's ratio. Both s(I) and s(II) phases have ultra-low Young's modulus, implying high flexibility. By applying a small tensile strain, s(II)-Au$_{2}$Te can be transformed into s(I)-Au$_{2}$Te. Hence, a structural phase transition from a room-temperature topological insulator to an auxetic semiconductor is found in the 2D forms of Au$_{2}$Te, which enables potential applications in phase-change electronic devices. Moreover, we elucidate the mechanism of the phase transition with the help of phonon spectra and group theory analysis.
We initiate a search for non-perturbative consistency conditions in M theory. Some non-perturbative conditions are already known in Type I theories; we review these and search for others. We focus principally on possible anomalies in discrete symmetries. It is generally believed that discrete symmetries in string theories are gauge symmetries, so anomalies would provide evidence for inconsistencies. Using the orbifold cosmic string construction, we give some evidence that the symmetries we study are gauged. We then search for anomalies in discrete symmetries in a variety of models, both with and without supersymmetry. In symmetric orbifold models we extend previous searches, and show in a variety of examples that all anomalies may be canceled by a Green-Schwarz mechanism. We explore some asymmetric orbifold constructions and again find that all anomalies may be canceled this way. Then we turn to Type IIB orientifold models where it is known that even perturbative anomalies are non-universal. In the examples we study, by combining geometric discrete symmetries with continuous gauge symmetries, one may define non-anomalous discrete symmetries already in perturbation theory; in other cases, the anomalies are universal. Finally, we turn to the question of CPT conservation in string/M theory. It is well known that CPT is conserved in all string perturbation expansions; here in a number of examples for which a non-perturbative formulation is available we provide evidence that it is conserved exactly.
A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-$\Delta$ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.
We investigate the emission mechanism and evolution of pulsars that are associated with supernova remnants.   We used imaging techniques in both the optical and near infrared, using images with very good seeing (<0.6) to study the immediate surroundings of the Crab pulsar. In the case of the infrared, we took two data sets with a time window of 75 days, to check for variability in the inner part of the Crab nebula. We also measure the spectral indices of all these wisps, the nearby knot, and the interwisp medium, using our optical and infrared data. We then compared the observational results with the existing theoretical models.   We report variability in the three nearby wisps located to the northwest of the pulsar and also in a nearby anvil wisp in terms of their structure, position, and emissivity within the time window of 75 days. All the wisps and the inner knot display red spectra with similar spectral indices. Similarly, the interwisp medium regions also show red spectra similar to those of the wisps. Also, based on archival HST data and our IR data, we find that the inner knot remains stationary for a time period of 13.5 years. The projected average velocity relative to the pulsar for this period is < 8 km/s.   By comparing the spectral indices of the structures in the inner Crab with the current theoretical models, we find that the Del Zanna et al. (2006) model for the synchrotron emission fits our observations, although the spectral index is at the flatter end of their modelled spectra.
The "no hair" theorem is not applicable to black holes formed from collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively "frozen-in" the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes N_B = e \Phi_\infty /(\pi c \hbar), where \Phi_\infty is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. The black hole's magnetosphere subsequently relaxes to the split monopole magnetic field geometry with self-generated currents outside the event horizon. The dissipation of the resulting equatorial current sheet leads to a slow loss of the anchored flux tubes, a process that balds the black hole on long resistive time scales rather than the short light-crossing time scales expected from the vacuum "no-hair" theorem.