Duality and integrability: Electromagnetism, linearized gravity and massless higher spin gauge fields as bi-Hamiltonian systems

Commutator identities on associative algebras and integrability of nonlinear pde's

It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to associate to such commutator identity both nonlinear equation and its Lax pair. Thus problem of construction of new integrable pde's reduces to construction of commutator identities on associative algebras.

A monoidal representation for linearized gravity

We propose an alternative representation for linear quantum gravity. It is based on the use of a structure that bears some resemblance to the Abelian loop representation used in electromagnetism but with the difference that space of extended object on which waves functions take values have a structure of commutative monoid instead of Abelian group. The generator of duality of the theory is realized in this representation and a geometrical interpretation is discussed.

How to use retarded Green's functions in de Sitter spacetime

We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in …

Integrability conditions of quasi-Newtonian cosmologies in modified gravity

We investigate the integrability conditions of a class of shear-free perfect-fluid cosmological models within the framework of anisotropic fluid sources, applying our results to f(R) dark energy models. Generalising earlier general relativistic results for time-like geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaitre-Robertson-Walker background and derive the equations that describe their dynamical evolutions. We show that in general, models with an anisotropic fluid source are…

Gapless Topological Order, Gravity, and Black Holes

In this work we demonstrate that linearized gravity exhibits gapless topological order with an extensive ground state degeneracy. This phenomenon is closely related both to the topological order of the pyrochlore U(1) spin liquid and to recent work by Hawking et. al. who used the soft photon and graviton theorems to demonstrate that the vacuum in linearized gravity is not unique. We first consider lattice models whose low-energy behavior are described by electromagnetism and linearized gravity, and then argue that the topological nature of these models carries over into the continuum. We demon…

史瓦西微扰理论的离壳对偶不变性

Off-shell duality invariance of Schwarzschild perturbation theory

该研究探究无旋转黑洞背景下麦克斯韦与线性化爱因斯坦-希尔伯特作用量的离壳对偶不变性，推导相关守恒律与恒等式，证明奇偶宇称度规微扰的Love数相等。