Symmetric superfluids

Abstract

We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincaré invariant scalar field theories that have an enlarged set of classically conserved currents at leading order in derivatives. These theories arise in the decoupling limit of the effective field theory of shift-symmetric, single-clock cosmologies and our results pick out all models with couplings fixed by additional symmetry. Remarkably, in D ≥ 2 spacetime dimensions there are only two possibilities: the Dirac-Born-Infeld theory and Scaling Superfluids with Lagrangian (−∂µφ∂ µ φ) α , for some real α. The scaling symmetry present for any α is further enhanced to the full conformal group only for α = D/2, and to infinitely many additional generators for the cuscuton, namely α = 1/2. We discuss the stability of Scaling Superfluids and point out that all coupling constants are determined by the speed of sound. * enrico.pajer@gmail.com † d.stefanyszyn@rug.nl 1 By "spacetime symmetries" we denote symmetries that do not commute with the Poincaré group.

Scale invariant solids

“…It isn't obvious whether one can construct an 'improved' traceless stress tensor [24][25][26][27][28], but it seems highly unlikely in the full nonlinear theory 2 . See [24,29] for discussions on this point in similar theories. Therefore these cases are scale but not conformal invariant (i.e.…”

“…It is easy to extend the the above analysis of solids that realize SI to a simpler case, namely a SI relativistic superfluid, which consists in a single scalar field that has a temporal vev for the gradient, Ψ = t + ψ. This case has also been studied in [29]. The most general action at leading order in derivatives is S = d d xP (X (Ψ) ) where X (Ψ) ≡ ∂ µ Ψg µν ∂ ν Ψ.…”

Accelerating universe with a stable extra dimension in cuscuton gravity

“…It belongs to a subclass of scalar-tensor theories where the Lorentz invariance is broken [18][19][20][21] and can be extended into more general class [22]. Aspects of symmetry in cuscuton gravity is studied in [23]. In particular, it has been shown that cuscuton gravity is useful in cosmology [24,25], for instance, a healthy bouncing solution without instabilities were realized [26].…”

Classification of symmetry breaking patterns in the theory of non-linear realizations

“…Consider the action S[φ] with a variational global symmetry group G and a vacuum solution φ 0 (x). In the active form, the symmetry group G acts on the fields φ(x) as 82) while the coordinates do not transform. A symmetry transformation for which g • φ 0 (x) = φ 0 (x) is broken by the vacuum field configuration.…”

“…Jacobi identities ensure that the algebra up to first-order is that of the four-dimensional conformal algebra. It is not possible to extend the conformal algebra with the addition of G 2 apart from in two space-time dimensions (see for [82] more details.). Due to the lack of shift symmetry and Adler's zero for the scalar, there is no sense in which the resulting EFT of the dilaton has an enhanced soft limit.…”