Related papers: Topologica Defects and Corrections to the Nambu Ac…

The most usual procedure for deriving curvature corrections to effective actions for topological defects is subjected to a critical reappraisal. A logically unjustified step (leading to overdetermination) is identified and rectified, taking…

We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero modes should be handled in…

Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…

By resorting to some results in quantum field theories with spontaneous breakdown of symmetry we show that an explanation based on microscopic dynamics can be given of the fact that topological defect formation is observed during the…

Using the Born-Oppenheimer approximation, we present a general description of topological defects dynamics in $p$-atic materials on curved surfaces, and simplify it in the case of active nematics. We find that activity induces a geometric…

Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss…

We study the low-energy effective action governing the transverse fluctuations of a long string, such as a confining flux tube in QCD. We work in the static gauge where this action contains only the transverse excitations of the string. The…

The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the…

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the…

Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…

Topological defects are a conspicuous feature of active liquid crystals that have been associated with important morphogenetic transitions in organismal development. Robust development thus requires a tight control of the motion and…

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…

We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional…

We study the dynamics of topological defects in active nematic films with spatially-varying activity and consider two setups: i) a constant activity gradient, and ii) a sharp jump in activity. A constant gradient of extensile (contractile)…

Biconformal gauging of the conformal group has a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dim scale-invariant polynomial actions and a dual action. We solve…

The self-propulsion of +1/2 topological defects is a hallmark of active nematic fluids, where the defects are advected by the flow field they themselves generate. In this paper we propose a minimal model for defect self-propulsion in a…

Cell layers are often categorized as contractile or extensile active nematics but recent experiments on neural progenitor cells with induced $+1$ topological defects challenge this classification. In a bottom-up approach, we first study a…

Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the 2D nematic and complex scalar field models.…

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here,…

We are studying quantum corrections in the earlier proposed string theory based on world-sheet action which measures the linear sizes of the surfaces. At classical level the string tension is equal to zero and as it was demonstrated in the…