The Collapse of Exotic Textures

The texture simulations below are being done in collaboration with Sean Carroll at MIT and Ted Pyne at the Harvard-Smithsonian Center for Astrophysics.

We have been studying the dynamics of a set of theories with broken symmetry which were classified by Bryan, Pyne and Carroll, all of which admit textures. Some of the theories admit other defects, such as monopoles, as well. Below, are movies of a slice through the three-dimensional texture (in some cases) and movies of 3-dimensional graphical representations of both the total and potential energies.

In the cases where slices are depicted, the modulus of the field in each theory is plotted. Actually, what is plotted is (1 - modulus); this is done, such that peaks in the plots correspond to defects, and low values mean that the field is near the potential minimum. In the 3-dimensional movies, an isosurface (in light blue) is plotted depicting the maximum of the potential energy density (and thus shows defects), and multicolored contours show the high energy region of the total energy density.

so(4) -> so(3)

This 3d movie shows a theory which admits only textures. The vacuum manifold in this theory is S^3. A massive wave of potential energy radiates away in a shell, as the total energy subsides at the core (and also radiates away, but the radiation is not seen).

so(3) -> so(2)

This movie shows a theory which admits monopoles as well as textures. The vacuum manifold is S^2. Here, we see that the initial configuration collapses, and forms monopoles. The vacuum manifold is S^2 in this theory.

so(4) -> u(2)

This movie shows a theory which admits monopoles as well as textures. The vacuum manifold is RP^2. Here, we see that the initial configuration collapses and forms monopoles. The vacuum manifold is RP^2 in this theory.

su(3) -> so(3)

This 3d movie shows a theory which admits monopoles with charge 0 and 1 (that is, monopoles with charge 2 are equivalent to the trivial configuration), and textures with charge 0, 1, 2, and 3. Note that monopoles are formed in this theory, but the modulus of the field does not go to zero. This indicates that these are monopoles which do not lie at |phi| = 0 (at the central peak in the potential), but somewhere else in the potential; this is possible because the theory is a tensor theory, and the potential has more invariants than the simple vector potential of, say so(3) -> so(2). The vacuum manifold is 5 dimensional in this theory.

so(5) -> so(3) x so(2) x Z_2

This movie shows a theory which admits monopoles and textures with charges 0 and 1. Notice that in this theory, even though monopoles are admitted, they do not form in the collapse. The collapse proceeds generating in two wavefronts, with final collapse after the second wavefront.

so(3) -> 0

This movie shows a theory which admits strings (with charges 0 and 1) and textures but no monopoles.

so(5) -> so(3)

This movie shows a theory which admits textures with charges 0 and 1. Notice that in this theory, a wave of massive radiation begins to expand out of the core of the collapse, then recollapses, then expands out again. This may be due to the limited charges in the theory.