Weirdest Martensite: Smectic Liquid Crystal Microstructure And Weyl-poincaré Invariance

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations. © 2016 American Physical Society.11

The length classification of threefold flops via noncommutative algebras

Smooth threefold flops with irreducible centres are classified by the length invariant, which takes values 1, 2, 3, 4, 5 or 6. This classification by Katz and Morrison identifies 6 possible partial resolutions of Kleinian singularities that can occur as generic hyperplane sections, and the simultaneous resolutions associated to such a partial resolution produce the universal flop of length l. In this paper we translate these ideas into noncommutative algebra. We introduce the universal flopping algebra of length l from which the universal flop of length l can be recovered by a moduli construction, and we present each of these algebras as the path algebra of a quiver with relations. This explicit realisation can then be used to construct examples of NCCRs associated threefold flops of any length as quiver with relations defined by superpotentials, to recover the matrix factorisation description of the universal flop conjectured by Curto and Morrison, and to realise examples of contraction algebras

Black holes in string theory with higher-derivative corrections

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 23-09-2020The low-energy limit of superstring theories admits a description in terms of an effective eld theory for its massless modes. The corresponding action is given by a double perturbative expansion in gs, the string coupling, and in 0, the square of the string length. The leading term of this expansion is given by one of the different ten-dimensional supergravity theories, whereas subleading terms involve terms of higher order in derivatives. The work presented in this thesis is the result of a research program that starts with the study of supersymmetric solutions of gauged supergravity and reaches the summit with the understanding of the effects produced by the 0 corrections to solutions of the heterotic superstring e ective action. This thesis is divided in two parts. The rst one focuses on the supersymmetric solutions of a minimal extension of the STU model of N = 1; d = 5 supergravity whose main interest lies on the fact that it can be obtained as a toroidal compacti cation of ten-dimensional N = 1 supergravity coupled to a triplet of SU(2) gauge elds. Concretely, we construct and study solutions describing black holes and smooth horizonless geometries with non-trivial Yang-Mills elds. The understanding of this type of solutions from the framework of string theory serves as a motivation for the work of the second part of the thesis, which is devoted to the study of solutions of the effective action of the heterotic string at rst order in 0. The latter does not simply coincide with the action of N = 1; d = 10 supergravity coupled to a Yang-Mills vector multiplet as the Green-Schwarz anomaly cancellation mechanism and supersymmetry enforce us to introduce additional terms in the action. These terms are constructed out of the spin connection with torsion given by the eld strength associated to the Kalb-Ramond 2-form and their contributions to the equations of motion are analogous to those of the Yang-Mills elds. This fact is exploited to construct analytic supersymmetric black-hole solutions with 0 corrections. The most important lesson to extract from our results is that the mass and the conserved charges of the black holes do get modi ed by the 0 corrections. This is what one would expect on physical grounds as the corrections act in the string equations of motion as effective sources of energy, momentum and charge. This information is crucial to establish a correspondence between the parameters that characterize the effective or coarse-grained description (the black hole) and those that characterize the microscopic system of string theory that it describes. The effects on the charges introduced by the higher-derivative corrections has a major impact in the understanding of the so-called small black holes, which are an effective description of a fundamental string with winding and momentum charges. Small black holes are singular solutions with vanishing horizon area in the supergravity approximation. It has long been believed that higher-derivative corrections would be able to stretch the horizon, making the solution regular. Our results reveal that this is not the case at rst order in 0, and that previous regularizations of heterotic small black holes actually describe a different microscopic system which is already regular in the supergravity approximation. The last chapter of the thesis contains the computation of the most general correction to the four-dimensional Kerr solution when the Einstein-Hilbert term is supplemented with higher curvature terms up to cubic order, including the possibility of having dynamical couplings. This general set-up includes, as a particular case, the corrections predicted by the heterotic superstring effective actio

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λGB. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N=4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λGB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy

Supercovergent sum-rules and the electromagnetic form-factors of elementary particles

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