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In this paper we study the dynamical generation of mass in the Lorentz-violating $CP^{(N-1)}$ model defined in two and three-dimensional aether-superspace. We show that even though the model presents a phase structure similar to the usual, Lorentz invariant case, the dynamically generated mass by quantum corrections has a dependence on the Lorentz violating background properties, except for spacelike LV vector parameter. This is to be contrasted with the behavior of the quantum electrodynamics in the two-dimensional aether-superspace, where the dynamical generation of mass was shown to exhibit an explicit dependence on the aether parameters in every possible case.
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Theories of low-energy Lorentz violation by a fixed-norm aether vector field with two-derivative kinetic terms have a globally bounded Hamiltonian and are perturbatively stable only if the vector is timelike and the kinetic term in the action takes the form of a sigma model. Here we investigate the phenomenological properties of this theory. We first consider the propagation of modes in the presence of gravity, and show that there is a unique choice of curvature coupling that leads to a theory without superluminal modes. Experimental constraints on this theory come from a number of sources, and we examine bounds in a two-dimensional parameter space. We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constant-density hypersurfaces in a Friedmann-Robertson-Walker cosmology. Finally, we examine cosmological evolution in the presence of an extra compact dimension of space, concluding that a vector can maintain a constant projection along the extra dimension in an expanding universe only when the expansion is exponential.
We analyze the two-dimensional CP(N-1) sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2D CP(N-1) sigma model in confinement phase, with a constant mass generated for the n(i) fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergravity since they look rather different between two approaches.
This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)), which implies that the super-Weyl transformations are generated by a covariantly chiral parameter instead of a real unconstrained one. We introduce various off-shell supermultiplets which are curved superspace analogues of the superconformal projective multiplets in global supersymmetry and which describe matter fields coupled to supergravity. A manifestly locally supersymmetric and super-Weyl invariant action principle is given. Off-shell locally supersymmetric nonlinear sigma models are presented in this new superspace.
We consider properties of the inhomogeneous solution found recently for mbox{$mathbb{CP}^{,N-1}$} model. The solution was interpreted as a soliton. We reevaluate its energy in three different ways and find that it is negative contrary to the previous claims. Hence, instead of the solitonic interpretation it calls for reconsideration of the issue of the true ground state. While complete resolution is still absent we show that the energy density of the periodic elliptic solution is lower than the energy density of the homogeneous ground state. We also discuss similar solutions for the ${mathbb{O}}(N)$ model and for SUSY extensions.
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