Vertex operators for cosmic strings

Skliros, Dimitri P (2011) Vertex operators for cosmic strings. Doctoral thesis (PhD), University of Sussex.

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Superstring theory posits that as complicated as nature may seem to the naive observer,
the variety of observed phenomena may be explained by postulating that at the fundamental
scale, matter is composed of lines of energy, namely strings. These oscillating lines
would be elementary and would hence have no substructure. They are expected to be incredibly tiny, their line-like structure would become noticeable at scales close to the string scale (which may lie anywhere from the TeV scale all the way up to the Planck scale) and would appear to be point-like to the macroscopic observer. Internal consistency then also requires the presence of higher dimensional objects, namely D-branes, all of which conspire and combine in such a way so as to give rise to the observable Universe. Advances in cosmology suggest the early universe was much hotter and denser than is the Universe at present, that the Universe has expanded and continues to expand (exponentially in fact) at present. This in turn has led a number of theorists to point out the remarkable possibility that some of these strings or D-branes were also stretched with the expansion. The resulting macroscopic strings, the so-called cosmic strings, would potentially stretch across the entire Universe.
Cosmic strings make their presence manifest by oscillating, scattering off other structures,
by decaying, producing gravitational waves and so on, and this in turn hints at
the available handles that may be used to observe them. Before we can hope to observe
cosmic strings however, the first step is then clearly to understand these properties which
determine their evolution. A number of approximate (classical) descriptions of cosmic
strings have been constructed to date, but approximations break down, especially when
potentially interesting things happen (e.g. close to cusps, i.e. points on the string that
reach the speed of light) and can obscure the physics. Thankfully, one can go beyond
these approximations: all properties of cosmic strings can be concisely and accurately
contained or encoded in a single object, the so-called fundamental cosmic string vertex
operator. In the present thesis I construct precisely this, covariant vertex operators for
general cosmic strings and this is the first such construction.
Cosmic strings, being macroscopic, are likely to exhibit classical behaviour in which
case they would most accurately be described by a string theory analogue of the well
known harmonic oscillator coherent states. By minimally extending the standard definition
of coherent states, so as to include the string theory requirements, I go on to construct
both open and closed covariant coherent state vertex operators. The naive construction
of the latter requires the existence of a lightlike compactification of spacetime. When the
lightlike winding states in the underlying Hilbert space are projected out, the resulting
vertex operators have a classical interpretation and can consistently propagate in noncompact spacetime. Using the DDF map I identify explicitly the corresponding general lightcone gauge classical solutions around which the exact macroscopic quantum states
are fluctuating. We go on to show that both the covariant gauge coherent vertex operators,
the corresponding lightcone gauge coherent states and the classical solutions all share
the same mass and angular momenta, which leads us to conjecture that the covariant and
lightcone gauge states are different manifestations of the same state and share identical interactions. Apart from the coherent state vertices I also present a complete set of covariant mass eigenstate vertex operators and these may also be relevant in cosmic string evolution. Finally, I also present the first amplitude computation with the coherent states, the graviton emission amplitude (including the effects of gravitational backreaction) for a simple class of cosmic string loops. As a byproduct of the above, I find that the fundamental building blocks of arbitrarily massive covariant string states are given by elementary Schur polynomials (equivalently complete Bell polynomials). This construction enables one to address the aforementioned questions concerning the properties of cosmic strings, their cosmological signatures, and may lead to the first observations of such objects in the sky. This in turn would be a remarkable way of verifying Superstring theory as the framework underlying the structure of our Universe.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics > QC0801 Geophysics. Cosmic physics
Depositing User: Library Cataloguing
Date Deposited: 10 Apr 2014 08:24
Last Modified: 18 Sep 2015 13:54

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