arXiv subjects

Rakibur Rahman

Publications and source records attributed to Rakibur Rahman.

At least 19 recordsLinked to original sources

arXiv2021

The Involutive System of Higher-Spin Equations

We revisit the problem of consistent free propagation of higher-spin fields in nontrivial backgrounds, focusing on symmetric tensor(-spinor)s. The Fierz-Pauli equations for massive fields in flat space form an involutive system, whose algebraic consistency owes to certain gauge identities. The zero mass limit of the former leads directly to massless higher-spin equations in the transverse-traceless gauge, where both the field and the gauge parameter have their respective involutive systems and gauge identities. In nontrivial backgrounds, it is the preservation of these gauge identities and symmetries that ensures the correct number of propagating degrees of freedom. With this approach we find consistent sets of equations for massive and massless higher-spin bosons and fermions in certain gravitational/electromagnetic backgrounds. We also present the involutive system of partially massless fields, and give an explicit form of their gauge transformations. We consider the Lie superalgebra of the operators on symmetric tensor(-spinor)s in flat space, and show that in AdS space the algebra closes nonlinearly and requires a central extension.

hep-th↗

arXiv2020

Stochastic Fractal and Noether's Theorem

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability $p$ or disappears with probability $1\!-\!p$. It describes a stochastic dyadic Cantor set that evolves in time, and eventually becomes a fractal. We investigate this phenomenon, through analytical methods and Monte Carlo simulation, for a generic class of models, where segment breakup points follow a symmetric beta distribution with shape parameter $α$, which also determines the fragmentation rate. For a fractal dimension $d_f$, we find that the $d_f$-th moment $M_{d_f}$ is a conserved quantity, independent of $p$ and $α$. We use the idea of data collapse -- a consequence of dynamical scaling symmetry -- to demonstrate that the system exhibits self-similarity. In an attempt to connect the symmetry with the conserved quantity, we reinterpret the fragmentation equation as the continuity equation of a Euclidean quantum-mechanical system. Surprisingly, the Noether charge corresponding to dynamical scaling is trivial, while $M_{d_f}$ relates to a purely mathematical symmetry: quantum-mechanical phase rotation in Euclidean time.

cond-mat.stat-mech↗

arXiv2019

The Uniqueness of Hypergravity

We show that consistent interactions of a spin-2 and a higher-spin Majorana fermion gauge fields in 3D flat space lead uniquely to Aragone-Deser hypergravity or its generalization. Our analysis employs the BRST-cohomological techniques, and works in the metric-like formulation under the assumptions of locality, parity and Poincaré invariance. Local hypersymmetry shows up as the unique consistent deformation of the gauge transformations. An extension of the theory with fermion flavors does not change these features, while a cosmological deformation becomes obstructed in the absence of other degrees of freedom and/or non-locality.

hep-th↗

arXiv2018

Gravitational Properties of the Proca Field

We study various properties of a Proca field coupled to gravity through minimal and quadrupole interactions, described by a two-parameter family of Lagrangians. Stückelberg decomposition of the effective theory spells out its model-dependent ultraviolet cutoff, parametrically larger than the Proca mass. We present pp-wave solutions that the model admits, consider linear fluctuations on such backgrounds, and thereby constrain the parameter space of the theory by requiring null-energy condition and the absence of negative time delays in high-energy scattering. We briefly discuss the positivity constraints$-$derived from unitarity and analyticity of scattering amplitudes$-$that become ineffective in this regard.

hep-th↗

arXiv2018

Spacetime Dimensionality from de Sitter Entropy

We argue that de Sitter universes with a small cosmological constant are entropically favored to have three spatial dimensions. The conclusion relies on the causal-patch description of de Sitter space, where fiducial observers experience local thermal equilibrium up to a stretched horizon, on the holographic principle, and on some assumptions about the nature of gravity and the constituents of Hawking/Unruh radiation.

hep-th↗

arXiv2018

Frame- and Metric-like Higher-Spin Fermions

Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone-Deser-Vasiliev frame-like formulation and the Fang-Fronsdal metric-like formulation. We review, clarify and elaborate on some essential features of these two. For frame-like free fermions in Anti-de Sitter space, one can present a gauge-invariant Lagrangian description such that the constraints on the field and the gauge parameters mimic their flat-space counterparts. This simplifies the explicit demonstration of the equivalence of the two formulations at the free level. We comment on the subtleties that may arise in an interacting theory.

hep-th↗

arXiv2017

Causality Constraints on Massive Gravity

The de Rham-Gabadadze-Tolley massive gravity admits pp-wave backgrounds on which linear fluctuations are shown to undergo time advances for all values of the parameters. The perturbations may propagate in closed time-like curves unless the parameter space is constrained to a line. These classical phenomena take place well within the theory's validity regime.

hep-th↗

arXiv2016

From Higher Spins to Strings: A Primer

A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincaré-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasiliev's equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the "central on-mass-shell theorem". These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.

hep-th↗

arXiv2016

Comments on Higher-Spin Fields in Nontrivial Backgrounds

We consider the free propagation of totally symmetric massive bosonic fields in nontrivial backgrounds. The mutual compatibility of the dynamical equations and constraints in flat space amounts to the existence of an Abelian algebra formed by the d'Alembertian, divergence and trace operators. The latter, along with the symmetrized gradient, symmetrized metric and spin operators, actually generate a bigger non-Abelian algebra, which we refer to as the "consistency" algebra. We argue that in nontrivial backgrounds, it is some deformed version of this algebra that governs the consistency of the system. This can be motivated, for example, from the theory of charged open strings in a background gauge field, where the Virasoro algebra ensures consistent propagation. For a gravitational background, we outline a systematic procedure of deforming the generators of the consistency algebra in order that their commutators close. We find that equal-radii AdSp X Sq manifolds, for arbitrary p and q, admit consistent propagation of massive and massless fields, with deformations that include no higher-derivative terms but are non-analytic in the curvature. We argue that analyticity of the deformations for a generic manifold may call for the inclusion of mixed-symmetry tensor fields like in String Theory.

hep-th↗

arXiv2016

A SUSY SU(6) GUT model with Pseudo-Goldstone Higgs Doublets

We present a novel way of realizing the pseudo-Nambu-Goldstone boson mechanism at all orders in perturbation theory, for the doublet-triplet splitting in supersymmetric grand unified theories. The global symmetries of the Higgs sector are attributed to a non-vectorlike Higgs content, which is consistent with unbroken supersymmetry in a scenario with flat extra dimensions and branes. We also show how in such a model one can naturally obtain a realistic pattern for the Standard Model fermion masses and mixings.

hep-ph↗

arXiv2015

Fermion Dipole Moment and Holography

In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued with superluminal modes. Requiring consistency of the dual CFT amounts to constraining the strength of the dipole coupling by an upper bound. We briefly discuss the implications of our results for the physics of holographic non-Fermi liquids.

hep-th↗

arXiv2014

Higher-Spin Modes in a Domain-Wall Universe

We find a consistent set of equations of motion and constraints for massive higher-spin fluctuations in a gravitational background, required of certain characteristic properties but more general than constant curvature space. Of particular interest among such geometries is a thick domain wall--a smooth version of the Randall-Sundrum metric. Apart from the graviton zero mode, the brane accommodates quasi-bound massive states of higher spin contingent on the bulk mass. We estimate the mass and lifetime of these higher-spin resonances, which may appear as metastable dark matter in a braneworld universe.

hep-th↗

arXiv2014

Gravitational Interactions of Higher-Spin Fermions

We investigate the cubic interactions of a massless higher-spin fermion with gravity in flat space and present covariant 2-s-s vertices, compatible with the gauge symmetries of the system, preserving parity. This explicit construction relies on the BRST deformation scheme that assumes locality and Poincare invariance. Consistent nontrivial cubic deformations exclude minimal gravitational coupling and may appear only with a number of derivatives constrained in a given range. Derived in an independent manner, our results do agree with those obtained from the light-cone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the non-Abelian ones are obstructed in a local theory beyond the cubic order.

hep-th↗

arXiv2013

Consistent Non-Minimal Couplings of Massive Higher-Spin Particles

The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach avoids this difficulty, but fails to ensure light-cone propagation and becomes very cumbersome. In this paper, we take an alternative route--the involutive form of the equations and constraints--to guarantee their algebraic consistency. This approach enormously simplifies the search for consistent interactions, now seen as deformations of the involutive system, by keeping manifest the causal propagation of the correct number of degrees of freedom. We consider massive particles of arbitrary integer spin in electromagnetic and gravitational backgrounds to find their possible non-minimal local couplings. Apart from easily reproducing some well-known results, we find restrictions on the backgrounds for consistent propagation of such a particle in isolation. The results can be altered by non-local interactions that may arise from additional massive states in the interacting theory.

hep-th↗

arXiv2013

Note on Gauge Invariance and Causal Propagation

Interactions of gauge-invariant systems are severely constrained by several consistency requirements. One is the preservation of the number of gauge symmetries, another is causal propagation. For lower-spin fields, the emphasis is usually put on gauge invariance that happens to be very selective by itself. We demonstrate with an explicit example, however, that gauge invariance, albeit indispensable for constructing interactions, may not suffice as a consistency condition. The chosen example that exhibits this feature is the theory of a massless spin-3/2 field coupled to electromagnetism. We show that this system admits an electromagnetic background in which the spin-3/2 gauge field may move faster than light. Requiring causal propagation rules out otherwise allowed gauge-invariant couplings. This emphasizes the importance of causality analysis as an independent test for a system of interacting gauge fields. We comment on the implications of allowing new degrees of freedom and non-locality in a theory, on higher-derivative gravity and Vasiliev's higher-spin theories.

hep-th↗

arXiv2013

Higher Spin Theory - Part I

These notes comprise a part of the introductory lectures on Higher Spin Theory presented in the Eighth Modave Summer School in Mathematical Physics. We construct free higher-spin theories and turn on interactions to find that inconsistencies show up in general. Interacting massless fields in flat space are in tension with gauge invariance and this leads to various no-go theorems. While massive fields exhibit superluminal propagation, appropriate non-minimal terms may cure such pathologies as they do in String Theory--a fact that we demonstrate. Given that any interacting massive higher-spin particle is described by an effective field theory, we compute a model independent upper bound on the ultraviolet cutoff in the case of electromagnetic coupling in flat space and discuss its implications. Finally, we consider various possibilities of evading the no-go theorems for massless fields, among which Vasiliev's higher-spin gauge theory is one. We employ the BRST-antifield method for a simple but non-trivial gauge system in flat space to find a non-abelian cubic coupling and to explore its higher-order consistency.

hep-th↗

arXiv2013

Holographic Constraints on a Vector Boson

We show that holography poses non-trivial restrictions on various couplings of an interacting field. For a vector boson in the AdS Reissner-Nordstrom background, the dual boundary theory is pathological unless its electromagnetic and gravitational multipole moments are constrained. Among others, a generic dipole moment afflicts the dual CFT with superluminal modes, whose remedy bounds the gyromagnetic ratio in a range around the natural value g=2. We discuss the CFT implications of our results, and argue that similar considerations can shed light on how massive higher-spin fields couple to electromagnetism and gravity.

hep-th↗

arXiv2013

Helicity-1/2 Mode as a Probe of Interactions of Massive Rarita-Schwinger Field

We consider the electromagnetic and gravitational interactions of a massive Rarita-Schwinger field. Stueckelberg analysis of the system, when coupled to electromagnetism in flat space or to gravity, reveals in either case that the effective field theory has a model-independent upper bound on its UV cutoff, which is finite but parametrically larger than the particle's mass. It is the helicity-1/2 mode that becomes strongly coupled at the cutoff scale. If the interactions are inconsistent, the same mode becomes a telltale sign of pathologies. Alternatively, consistent interactions are those that propagate this mode within the light cone. Studying its dynamics not only sheds light on the Velo-Zwanziger acausality, but also elucidates why supergravity and other known consistent models are pathology-free.

hep-th↗