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We show that a large class of null electromagnetic fields are immune to any modifications of Maxwells equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.
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We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor $T_{mu u}$ constructed from sums of terms the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called {it universal} if, when evaluated on that Einstein metric, $T_{mu u}$ is a multiple of the metric. A Ricci flat classical solution is called {it strongly universal} if, when evaluated on that Ricci flat metric, $T_{mu u}$ vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalisation; Einstein metrics with holonomy ${rm Sim} (n-2)$ in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalised Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all 4-dimensional ${rm Sim}(2)$ Einstein metrics. We also discuss generalizations to higher dimensions.
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.
Field theory models of axion monodromy have been shown to exhibit vacuum energy sequestering as an emergent phenomenon for cancelling radiative corrections to the cosmological constant. We study one loop corrections to this class of models coming from virtual axions using a heat kernel expansion. We find that the structure of the original sequestering proposals is no longer preserved at low energies. Nevertheless, the cancellation of radiative corrections to the cosmological constant remains robust, even with the new structures required by quantum corrections.
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.
We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(boldsymbol{g},boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of Lagrangian theories including both modified gravities and (possibly non-minimally coupled) modified electrodynamics. Specifically, both $boldsymbol{g}$ and $boldsymbol{F}$ are fields with vanishing scalar invariants and further satisfy two simple tensorial conditions. They describe a family of gravitational and electromagnetic plane-fronted waves of the Kundt class and of Weyl type III (or more special). The local form of $(boldsymbol{g},boldsymbol{F})$ and a few examples are also provided.
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