An Action for Extended String Newton-Cartan Gravity

We construct an action for four-dimensional extended string Newton-Cartan gravity which is an extension of the string Newton-Cartan gravity that underlies nonrelativistic string theory. The action can be obtained as a nonrelativistic limit of the Einstein-Hilbert action in General Relativity augmented with a term that contains an auxiliary two-form and one-form gauge field that both have zero flux on-shell. The four-dimensional extended string Newton-Cartan gravity is based on a central extension of the algebra that underlies string Newton-Cartan gravity. The construction is similar to the earlier construction of a three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which is based on a central extension of the algebra that underlies Newton-Cartan gravity. We show that this three-dimensional action is naturally obtained from the four-dimensional action by a reduction over the spatial isometry direction longitudinal to the string followed by a truncation of the extended string Newton-Cartan gravity fields. Our construction can be seen as a special case of the construction of an action for extended p-brane Newton-Cartan gravity in p+3 dimensions.Comment: 16 pages; v2: references added; v3: 18 pages, published versio

Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons

We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance, and study technical Naturalness of Nambu-Goldstone (NG) modes whose dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents $z>1$. For example, we find NG modes with a technically natural quadratic dispersion relation which do not break time reversal symmetry and are associated with a single broken symmetry generator, not a pair. The mechanism is protected by an enhanced `polynomial shift' symmetry in the free-field limit.Comment: 5 pages, 1 figure; v2: minor typos corrected, references adde

Software Defined Radio Implementation of Carrier and Timing Synchronization for Distributed Arrays

The communication range of wireless networks can be greatly improved by using distributed beamforming from a set of independent radio nodes. One of the key challenges in establishing a beamformed communication link from separate radios is achieving carrier frequency and sample timing synchronization. This paper describes an implementation that addresses both carrier frequency and sample timing synchronization simultaneously using RF signaling between designated master and slave nodes. By using a pilot signal transmitted by the master node, each slave estimates and tracks the frequency and timing offset and digitally compensates for them. A real-time implementation of the proposed system was developed in GNU Radio and tested with Ettus USRP N210 software defined radios. The measurements show that the distributed array can reach a residual frequency error of 5 Hz and a residual timing offset of 1/16 the sample duration for 70 percent of the time. This performance enables distributed beamforming for range extension applications.Comment: Submitted to 2019 IEEE Aerospace Conferenc