Low-energy propagation modes on string network

Abstract

We study low-energy propagation modes on string network lattice. Specifically, we consider an infinite two-dimensional regular hexagonal string network and analyze the low frequency propagation modes on it. The fluctuation modes tangent to the two-dimensional plane respect the spatial rotational symmetry on the plane, and are described by Maxwell theory. The gauge symmetry comes from the marginal deformation of changing the sizes of the loops of the lattice. The effective Lorentz symmetry respected at low energy will be violated at high energy. *

Geometry on string lattice

“…This solution exists for any momenta (p 1 , p 2 ) without any cost of energy: ω = 0. These modes were identified as the gauge symmetry of the low energy effective action in our previous paper [8]. The reason for this identification is that this fact shows that these modes are the time-independent local deformations of the string lattice configuration under which the potential energy remains unchanged.…”

“…Since these zero modes exist locally in a string network, it is generally an object which can have a macroscopic entropy [7]. In this paper, we will continue pursuing the possibility whether a string lattice can be regarded as a kind of continuous space in the low energy limit [8], like in lattice gauge theory. This way of view might be similar in spirit to the idea of brane world [9,10] and also to the network appearing in quantum gravity [11,12,13,14,15].…”

“…The dynamics of a string network was analyzed in the small oscillation limit in [16,17], and a general framework for studying the moduli space of the above mentioned zero modes was recently given in [18]. The question of what kind of field theory is on a string lattice was studied in our previous paper [8] for the case of a regular hexagonal lattice. There the oscillations of a string lattice is approximated by the oscillations of junctions between which there are straight strings.…”

“…The approximate treatment in our previous paper [8] can be well controlled by assigning a point-like mass to each junction. If we take the mass sufficiently large, the oscillations of the junctions will become sufficiently slower than the string oscillations, which will validate our approximation.…”

“…In this paper we will instead use the method developed in [17] to investigate the low energy dynamics of a periodic string lattice, and will generalize our previous results [8]. In section 2, we will recapitulate and discuss some properties of the scattering matrix associated to junctions and the low energy oscillation modes on a string lattice.…”