R-symmetry Charges of Monopole Operators
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Typ
Examensarbete för masterexamen
Master Thesis
Master Thesis
Program
Publicerad
2010
Författare
Lindkvist, Joel
Modellbyggare
Tidskriftstitel
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Sammanfattning
M-theory is an attempt to unify the different 10-dimensional superstring theories in a single framework. In this 11-dimensional theory the strings be- come two-dimensional objects called M2-branes. The interactions of these branes are not very well understood at a fundamental level. At low ener- gies, however, a three-dimensional superconformal field theory known as the ABJM theory has been conjectured to describe the world-volume dynamics of multiple M2-branes. We introduce monopole operators in three-dimensional field theories and calculate the R-symmetry charges of such operators in N = 3 Chern-Simons Yang-Mills theory. This theory reduces to the ABJM theory in the IR, but our calculations are performed in the UV. Results for the ABJM case can be obtained by flowing to the IR, if the quantities involved are constant along the RG flow. Monopole operators with vanishing R-charges are needed in the ABJM theory, both for supersymmetry enhancement and for matching the spectrum with the dual gravity theory. To describe the monopole operators we use the radial quantization method, allowing us to indirectly study the operators by looking at monopole states. We start by calculating the abelian R-charges carried by our monopole vacuum state. This is done by a normal ordering computation and proves that there exist monopoles with vanishing R-charge. Since the abelian charge can change along the RG flow, however, this does not prove anything for the ABJM the- ory. The non-abelian SU(2)R-charges are calculated by studying the collective coordinate parametrizing our monopole vacuum state. These charges are also found to be vanishing, and since non-abelian representations cannot change continuously the result is valid in the IR (ABJM) limit as well. As a part of our computations we also derive explicit expressions for the monopole spinor harmonics, defined as eigenspinors of the Dirac operator on a sphere around a magnetic monopole.
Beskrivning
Ämne/nyckelord
Grundläggande vetenskaper , Elementarpartikelfysik , Basic Sciences , Elementary particle physics