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Blagoje Oblak

Publications and source records attributed to Blagoje Oblak.

33 records · Page 2Linked to original sources
arXiv2020

Orbital Bifurcations and Shoaling of Cnoidal Waves

We study the parameter space of cnoidal waves -- the periodic solitons of the Korteweg-de Vries equation -- from the perspective of Virasoro coadjoint orbits. The monodromy method familiar from inverse scattering implies that many, but not all, of these solitons are conformally equivalent to uniform field configurations (constant coadjoint vectors). The profiles that have no uniform representative lie in Lamé band gaps and are separated from the others by bifurcation lines along which the corresponding orbits change from elliptic to hyperbolic. We show that such bifurcations can be produced by shoaling: wave profiles become non-uniformizable once their pointedness parameter crosses a certain critical value (which we compute). As a by-product, we also derive asymptotic relations between the pointedness and velocity of cnoidal waves along orbital level curves.

math.AP↗
arXiv2020

Hirota-Satsuma Dynamics as a Non-Relativistic Limit of KdV Equations

We consider a system of two coupled KdV equations (one for left-movers, the other for right-movers) and investigate its ultra-relativistic and non-relativistic limits in the sense of BMS$_3$/GCA$_2$ symmetry. We show that there is no local ultra-relativistic limit of the system with positive energy, regardless of the coupling constants in the original relativistic Hamiltonian. By contrast, local non-relativistic limits with positive energy exist, provided there is a non-zero coupling between left- and right-movers. In these limits, the wave equations reduce to Hirota-Satsuma dynamics (of type IV) and become integrable. This is thus a situation where input from high-energy physics contributes to nonlinear science - in this case, uncovering the limiting relation between integrable structures of KdV and Hirota-Satsuma.

hep-th↗
arXiv2018

From the Lorentz Group to the Celestial Sphere

In these lecture notes we review the isomorphism between the (connected) Lorentz group and the set of conformal transformations of the sphere. More precisely, after establishing the main properties of the Lorentz group, we show that it is isomorphic to the group SL(2,C) of complex 2 by 2 matrices with unit determinant. We then classify conformal transformations of the sphere, define the notion of null infinity in Minkowski space-time, and show that the action of Lorentz transformations on the celestial spheres at null infinity is precisely that of conformal transformations. In particular, we discuss the optical phenomena observed by the pilots of the "Millenium Falcon" during the jump to lightspeed.

math-ph↗
arXiv2018

BMS Particles in Three Dimensions

This thesis is devoted to the group-theoretic aspects of three-dimensional quantum gravity on Anti-de Sitter and Minkowskian backgrounds. In particular we describe the relation between unitary representations of asymptotic symmetry groups and gravitational perturbations around a space-time metric. In the asymptotically flat case this leads to "BMS particles", representing standard relativistic particles dressed with gravitational degrees of freedom accounted for by coadjoint orbits of the Virasoro group. Their thermodynamics are described by BMS characters, which coincide with gravitational one-loop partition functions. We also extend these considerations to higher-spin theories and supergravity.

hep-th↗
arXiv2018

Thomas Precession for Dressed Particles

We consider a particle dressed with boundary gravitons in three-dimensional Minkowski space. The existence of BMS transformations implies that the particle's wavefunction picks up a Berry phase when subjected to changes of reference frames that trace a closed path in the asymptotic symmetry group. We evaluate this phase and show that, for BMS superrotations, it provides a gravitational generalization of Thomas precession. In principle, such phases are observable signatures of asymptotic symmetries.

hep-th↗
arXiv2017

Berry Phases on Virasoro Orbits

We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed exactly thanks to the Maurer-Cartan form on the Virasoro group, and they persist after combining left- and right-moving sectors. Thinking of Virasoro representations as particles in AdS_3 dressed with boundary gravitons, the Berry phases associated with Brown-Henneaux diffeomorphisms provide a gravitational extension of Thomas precession.

hep-th↗
arXiv2017

Probing Wigner Rotations for Any Group

Wigner rotations are transformations that affect spinning particles and cause the observable phenomenon of Thomas precession. Here we study these rotations for arbitrary symmetry groups with a semi-direct product structure. In particular we establish a general link between Wigner rotations and Thomas precession by relating the latter to the holonomies of a certain Berry connection on a momentum orbit. Along the way we derive a formula for infinitesimal, Lie-algebraic transformations of one-particle states.

hep-th↗
arXiv2016

Rotating Higher Spin Partition Functions and Extended BMS Symmetries

We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincaré characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms_3 algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated characters. We also extend our investigations to supergravity and to a class of gauge theories involving higher-spin fermionic fields.

hep-th↗
arXiv2016

BMS Modules in Three Dimensions

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and W algebras, which is to be contrasted with non-relativistic limits that typically give non-unitary representations. To support this dichotomy, we also point out that the ultrarelativistic and non-relativistic limits of generic W algebras differ in the structure of their non-linear terms.

hep-th↗
arXiv2016

Near-Horizon Geometry and Warped Conformal Symmetry

We provide boundary conditions for three-dimensional gravity including boosted Rindler spacetimes, representing the near-horizon geometry of non-extremal black holes or flat space cosmologies. These boundary conditions force us to make some unusual choices, like integrating the canonical boundary currents over retarded time and periodically identifying the latter. The asymptotic symmetry algebra turns out to be a Witt algebra plus a twisted u(1) current algebra with vanishing level, corresponding to a twisted warped CFT that is qualitatively different from the ones studied so far in the literature. We show that this symmetry algebra is related to BMS by a twisted Sugawara construction and exhibit relevant features of our theory, including matching micro- and macroscopic calculations of the entropy of zero-mode solutions. We confirm this match in a generalization to boosted Rindler-AdS. Finally, we show how Rindler entropy emerges in a suitable limit.

hep-th↗
arXiv2015

Characters of the BMS Group in Three Dimensions

Using the Frobenius formula, we evaluate characters associated with certain induced representations of the centrally extended BMS$_3$ group. This computation involves a functional integral over a coadjoint orbit of the Virasoro group; a delta function localizes the integral to a single point, allowing us to obtain an exact result. The latter is independent of the specific form of the functional measure, and holds for all values of the BMS$_3$ central charges and all values of the chosen mass and spin. It can also be recovered as a flat limit of Virasoro characters.

hep-th↗
arXiv2015

Notes on the BMS group in three dimensions: II. Coadjoint representation

The coadjoint representation of the BMS$_3$ group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS$_3$ orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, the link with induced representations upon geometric quantization is discussed.

hep-th↗
arXiv2014

Holographic positive energy theorems in three-dimensional gravity

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the behavior of the energy functional on these orbits can be used to discuss positive energy theorems.

hep-th↗
arXiv2014

Notes on the BMS group in three dimensions: I. Induced representations

The Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the circle with the space of its adjoint representation, embedded as an abelian normal subgroup. The structure of the group suggests to study induced representations; we show here that they are associated with the well-known coadjoint orbits of the Virasoro group and provide explicit representations in terms of one-particle states.

hep-th↗