Hello everyone,
My name is Jessica Barrett, and I am currently working as a postdoc at the Institute of Theoretical Physics of TUWien, in the string theory group of Prof. Maximilian Kreuzer. I would like to thank the Erwin Schrodinger Institute of Mathematical Physics, which is funding me as a Junior Research Fellow, for giving me the opportunity to come to Vienna and collaborate with the group here. In September 2004, before arriving in Vienna, I completed my PhD at the University of Durham; my supervisor there was Dr. Peter Bowcock, and while there I also worked with Prof. Clifford Johnson.
To begin with I would like to say a few words about string theory in general. String theory currently appears to be the most promising candidate for unifying the four fundamental forces of nature; closed strings (i.e. strings with two ends joined together to make a loop) give rise to the gravitational force, and gauge theory forces can be obtained from open strings (strings with two free ends). However, no one as yet has been able to derive a realistic low energy model, i.e. the Standard Model, from string theory. One of the main obstacles is that string theory only works in a spacetime with ten dimensions, and so we need a mechanism to explain why we only see four in our world. We usually achieve this by compactifying the extra dimensions on some manifold, which must be small so that they are not normally visible. It was realised, around ten years ago, that string theory contains not only strings, but also higher-dimensional objects called Dp-branes, where p is the number of spatial dimensions of the brane. The defining property of a Dp-brane is that the end of an open string is constrained to lie on its surface. D-branes appear to hold the key to obtaining a realistic model from string theory, because on the surface of the D-brane there is a gauge theory, with the ends of the open strings acting as the gauge bosons of the theory. The construction of D-brane configurations therefore allows us to construct gauge theories in string theory, and so an understanding of the many and varied ways in which D-branes interact with one another is an essential step towards constructing a realistic model from string theory. It is important, therefore, that we continue to learn more about D-branes. This was the motivation behind the work I did for my PhD. The full title of my PhD thesis was 'Aspects of D-Branes as BPS Monopoles'.
I will next give some brief words of introduction to the theory of magnetic monopoles. Introducing magnetic charge and magnetic current into Maxwell's equations gives a theory of electromagnetism which contains magnetic monopoles, as well as electric monopoles. This may seem a strange thing to do, as magnetic monopoles have not been observed experimentally. However, they are an interesting phenomena to consider because the presence of magnetic monopoles provides an explanation for the quantisation of electric charge (as was originally observed by Dirac). Moreover, their mass is inversely proportional to the electric charge, and so they may simply be too heavy to observe experimentally at the current time. Magnetic monopoles also appear as topological solitons of Yang-Mills-Higgs theory. The BPS monopole from the title of my thesis is given by taking a certain limit of a Yang-Mills-Higgs monopole, and obeys the relation that its mass is proportional to its charge.
In my PhD thesis I studied two examples of D-brane configurations which behave as magnetic monopoles. The first was D1-branes (i.e. a stringlike brane - recall that the 1 here refers to the number of spatial dimensions of the brane), which were stretched between two parallel D3-branes. The end of the D1-brane looks like a BPS monopole from the point of view of the gauge theory on the D3-brane. This configuration can be studied from two alternative perspectives; using the D3-brane action (in which the D1-brane appears as a solitonic solution), or using the D1-brane action (in which the D3-brane appears as a solitonic solution). The idea behind my research, which was carried out in collaboration with Dr. Bowcock, was to perform a calculation from the D1-brane perspective, whose result was already known from the D3-brane perspective (the gauge theory on the D3-branes is (3+1)-dimensional SU(2) Yang-Mills-Higgs theory, with the distance between the D3-branes playing the role of the Higgs field). More specifically, we calculated the energy radiated during the scattering of two D1-branes stretched between the D3-branes. Results from the scattering of two SU(2) BPS monopoles suggest that the answer should be of the order of 17v^5, where v is the initial velocity of he monopoles. However, our results from the D1-brane perspective suggest that there is no energy radiated during scattering. The origin of the discrepancy between these two results is currently unclear.
The second D-brane configuration which I studied for my PhD thesis was a D6-brane with four dimensions wrapped on a K3 manifold. This work was carried out in collaboration with Prof. Johnson. When a D6-brane is wrapped on a K3 manifold, curvature corrections to the action imply that there is induced some negative D2-brane charge. The resulting object, which has negative D2-brane and positive D6-brane charges, is known as the enhancon for reasons that will shortly become clear. Transverse to the brane directions there are three spatial dimensions. In these dimensions the enhancon is thought to behave like a BPS monopole. This is because the object obtained by wrapping a D4-brane on a K3 manifold, which is the magnetic dual to the D6-D2 object in the same way that an electron is the magnetic dual to the magnetic monopole, can correspond to the gauge boson of a U(1) gauge symmetry. This D4-D0 object becomes massless at the core of the enhancon, which is an indication that the U(1) symmetry is enhanced to an SU(2) symmetry there (hence the name enhancon!). This symmetry enhancement is an indication that the enhancon behaves as a BPS monopole (which also contains at its core a region where SU(2) symmetry is restored, because the Higgs field is zero there). In the enhancon scenario the volume of the K3 manifold corresponds to the Higgs field of the BPS monopole. The calculation we carried out was to calculate the metric on moduli space of many enhancons in the limit that they are far apart from one another (i.e. the metric of the manifold whose dimensions are the parameters of the enhancon solution). We found that this metric was indeed identical to the metric on moduli space of many BPS monopoles, as we expected from the arguments given above.
In collaboration with the string theory group of TUWien, I have recently been studying a slightly different area, although one closely related to my previous research. We would like to understand branes compactified on manifolds when the compactification scale is small. Of particular phenomenological interest is the case when the manifold is a Calabi-Yau manifold. The branes can either wrap the full manifold or some cycles of the manifold. Hopefully I will have more to say on this subject at some point in the future!
References:
[1] J.K.Barrett and C.V.Johnson, "Wrapped D-branes as BPS monopoles: The moduli space perspective", Phys.Rev.D 69 (2004) 126005, arXiv:hep-th/0312053.
[2] J.K.Barrett and P.Bowcock, "Using D-strings to describe monopole scattering", arXiv:hep-th/0402163.
[3] J.K.Barrett and P.Bowcock, "Using D-strings to describe monopole scattering: numerical results" (to appear).
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