We consider a Bose-Einstein condensate interacting with a gravitational wave for the case when the gravitational fluctuations are quantized in order to incorporate quantum gravity effects into the theory. We observe that the solution of the time-dependent part of the pseudo-Goldstone boson has infusions from the noise induced by gravitons and the corresponding differential equation of motion is Langevin-like. Using this result, we obtain the quantum gravity modified Fisher information which has been termed as the quantum gravitational Fisher information (QGFI). The inverse square root of the stochastic average of the QGFI gives the minimum uncertainty in the measurement of the gravitational wave amplitude. The minimum uncertainty does not go to infinity as the measurement time approaches zero in a quantum gravity setup rather it has a measurable finite value for gravitons with high squeezing. Finally, we observe the effect of decoherence due to interacting phonon modes in the QGFI and observe a less obvious decoherence effect for higher squeezing of the initial graviton.
Following hep-th/0412336 we use the non-linear realisation of the semi-direct product of E11 and its vector representation to construct brane dynamics. The brane moves through a spacetime which arises in the non-linear realisation from the vector representation and it contains the usual embedding coordinates as well as the world volume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full E11 symmetry and so the Cremmer-Julia duality symmetries. We apply this theory to find the dynamics of the IIA and IIB strings, the M2 and M5 branes, the IIB D3 brane as well as the one and two branes in seven dimensions.
The non-linear realisation of the semi-direct product of E11 with its vector representation leads to equation of motions for the fields graviton, three form, six form, dual graviton and the level four fields which correctly describe the degree of freedom of eleven dimensional supergravity at the linearised level. The equations with one derivative generically hold as equivalence relations and are often duality relations. From these equations, by taking derivatives, one can derive equations that are equations of motion of the familiar kind. The entire hierarchy of equations is E11 invariant and the construction does not require any steps beyond E11. We review these past developments with an emphasis on the features that have been overlooked in hep-th:1703.01305, whose alternative approach we also comment on.
Recently a BPS Alice string has been found in a $$U(1)\times SO(3)$$U(1)×SO(3) gauge theory coupled with three charged complex scalar fields in the triplet representation (in JHEP 1709:046 arXiv:1703.08971 [hep-th], 2017). It is a half BPS state preserving a half of the supercharges when embedded into a supersymmetric gauge theory. In this paper, we study zero modes of a BPS Alice string. After presenting U(1) and translational zero modes, we construct the effective action of these modes. In contrast to a previous analysis of the conventional Alice string for which only large distance behaviors are known, we can exactly perform a calculation in the full space thanks to the BPS properties.