arXiv subjects

Paul K. Townsend

Publications and source records attributed to Paul K. Townsend.

At least 37 records · Page 2Linked to original sources

arXiv2019

DBI in the IR

The IR limit of a planar static D3-brane in AdS5 x S5 is a tensionless D3-brane at the AdS horizon, with dynamics governed by a strong-field limit of the Dirac-Born-Infeld action analogous to that found from the Born-Infeld action by Bialynicki-Birula. As in that case, the field equations are those of an interacting 4D conformal invariant field theory with an Sl(2;R) electromagnetic duality invariance, but the D3-brane origin makes these properties manifest. We also find an Sl(2;R)-invariant action for these equations.

hep-th↗

arXiv2019

On asymptotic charges in 3D gravity

A variant of the ADT method for the determination of gravitational charges as integrals at infinity is applied to "Chern-Simons-like" theories of 3D gravity, and the result is used to find the mass and angular momentum of the BTZ black hole considered as a solution of a variety of massive 3D gravity field equations. The results agree with many obtained previously by other methods, including our own results for "Minimal Massive Gravity", but they disagree with others, including recently reported results for "Exotic Massive Gravity". We also find the central charges of the asymptotic conformal symmetry algebra for the generic 3D gravity model with AdS vacuum and discuss implications for black hole thermodynamics.

hep-th↗

arXiv2018

Exotic Massive 3D Gravity

The linearized equations of `New Massive Gravity' propagate a parity doublet of massive spin-2 modes in 3D Minkowski spacetime, but a different non-linear extension is made possible by `third-way' consistency. There is a `Chern-Simons-like' action, as for other 3D massive gravity models, but the new theory is `exotic': its action is parity odd. This `Exotic Massive Gravity' is the next-to-simplest case in an infinite sequence of third-way consistent 3D gravity theories, the simplest being the `Minimal Massive Gravity' alternative to `Topologically Massive Gravity'.

hep-th↗

arXiv2018

Gravity and the spin-2 planar Schroedinger equation

A Schroedinger equation proposed for the GMP gapped spin-2 mode of fractional Quantum Hall states is found from a novel non-relativistic limit, applicable only in 2+1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3+1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the non-linear Einstein equations, a confining harmonic oscillator potential for the individual particles.

hep-th↗

arXiv2018

On nonrelativistic 3D Spin-1 theories

We describe non-relativistic limits of the 3D Proca and square-root Proca theories that yield spin-1 Schroedinger equations. Analogous results are found by generalized null reduction of the 4D Maxwell or complex self-dual Maxwell equations. We briefly discuss the extension to spin-2.

hep-th↗

arXiv2017

Twistor description of spinning particles in AdS

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D=4,5,7, which linearises invariance under the AdS isometry group Sp(4;K) for K=R,C,H, is generalized to the massless N-extended "spinning particle". The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS_5.

hep-th↗

arXiv2017

Pauli-Lubanski, Supertwistors, and the Superspinning Particle

We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a "superspinning particle" of superspin 1/2. We then use an Sl(2;K)-spinor formalism for K=R,C,H to unify our 4D results with previous results for 3D and 6D (super)Pauli-Lubanski tensors.

hep-th↗

arXiv2017

Tachyons in the Galilean limit

The Souriau massless Galilean particle of "colour" $k$ and spin $s$ is shown to be the Galilean limit of the Souriau tachyon of mass $m = ik$ and spin $s$. We compare and contrast this result with the recent Galilean limit of the Nambu-Goto string and the Green-Schwarz superstring.

hep-th↗

arXiv2017

Anti-de Sitter particles and manifest (super)isometries

Starting from the classical action for a spin-zero particle in a D-dimensional anti-Sitter (AdS) spacetime, we recover the Breitenlohner-Freedman bound by quantization. For D=4,5,7, and using an Sl(2;K) spinor notation for K=R,C,H, we find a bi-twistor form of the action for which the AdS isometry group is linearly realised, although only for zero mass when D=4,7, in agreement with previous constructions. For zero mass and D=4, the conformal isometry group is linearly realized. We extend these results to the superparticle in the maximally supersymmetric "AdS x S" string/M-theory vacua, showing that quantization yields a 128+128 component supermultiplet. We also extend them to the null string.

hep-th↗

arXiv2017

The Galilean Superstring

The action for a Galilean superstring is found from a non-relativistic limit of the closed Green-Schwarz (GS) superstring; it has zero tension and provides an example of a massless super-Galilean system A Wess-Zumino term leads to a topological central charge in the Galilean supersymmetry algebra, such that unitarity requires a upper bound on the total momentum. This Galilean-invariant bound, which is also implied by the classical phase-space constraints, is saturated by solutions of the superstring equations of motion that half-preserve supersymmetry. We discuss briefly the extension to the Galilean supermembrane.

hep-th↗

arXiv2016

The Jordan formulation of Quantum Mechanics: a review

This is a transcription of a conference proceedings from 1985. It reviews the Jordan algebra formulation of quantum mechanics. A possible novelty is the discussion of time evolution; the associator takes over the role of $i$ times the commutator in the standard density matrix formulation, and for the Jordan algebra of complex Hermitian matrices this implies a Hamiltonian of the form $H= i[x,y] + λ\mathbb{I}$ for traceless Hermitian $x,y$ and real number $λ$. Other possibilities for time evolution in the Jordan formulation are briefly considered.

quant-ph↗

arXiv2016

Worldline CPT and massless supermultiplets

The action for a massless particle in 4D Minkowski space has a worldline time-reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the N-extended superparticle is shown to be anomalous when N is odd, in the supertwistor formalism this is because a CPT-violating worldline-Chern-Simons term is needed to preserve the chiral U(1) gauge invariance. This accords with the fact that no massless N=1 super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when N is even, but it has $2^{N+1}$ states when N/2 is odd (e.g. the N=2 hypermultiplet) in contrast to just $2^N$ when N/2 is even (e.g. the N=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when N/2 is odd.

hep-th↗

arXiv2016

Noether theorems and higher derivatives

A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $ε$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dotε$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\ddot ε$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered and the extension to field theory discussed.

hep-th↗

arXiv2015

Twistors and the massive spinning particle

Gauge-invariant twistor variables are found for the massive spinning particle with N-extended local worldline supersymmetry, in spacetime dimensions D=3,4,6. The twistor action is manifestly Lorentz invariant but the anticommuting spin variables appear exactly as in the non-relativistic limit. This allows a simple confirmation that the quantum N=2 spinning particle has either spin one or spin zero, and that N>2 is quantum inconsistent for D=4,6.

hep-th↗

arXiv2015

Twistor form of massive 6D superparticle

The massive six-dimensional (6D) superparticle with manifest (n,0) supersymmetry is shown to have a supertwistor formulation in which its "hidden" (0,n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin, for n=1 it propagates the 6D Proca supermultiplet.

hep-th↗

arXiv2015

The Third Way to 3D Gravity

Consistency of Einstein's gravitational field equation $G_{μν} \propto T_{μν}$ imposes a "conservation condition" on the $T$-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion, and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a "non-geometrical" action: one {\it not} constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D "minimal massive gravity" model, which resolves the "bulk vs. boundary" unitarity problem of topologically massive gravity with anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher-dimensional theories.

gr-qc↗

arXiv2015

Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieved in the "third way" exploited by 3D "minimal massive gravity". We relate our results to the "novel Higgs mechanism" for Chern-Simons gauge theories.

hep-th↗

arXiv2015

Minimal Massive 3D Gravity Unitarity Redux

A geometrical analysis of the bulk and anti-de Sitter boundary unitarity conditions of 3D "Minimal Massive Gravity" (MMG) (which evades the "bulk/boundary clash" of Topologically Massive Gravity) is used to extend and simplify previous results, showing that unitarity selects, up to equivalence, a connected region in parameter space. We also initiate the study of flat-space holography for MMG. Its relevant flat space limit is a deformation of 3D conformal gravity; the deformation is both non-linear and non-conformal, implying a linearisation instability.

hep-th↗