Five-brane BPS states in heterotic M-theory

Abstract

We present explicit methods for computing the discriminant curves and the associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau threefolds.These methods are applied to a specific three-family, SU (5) grand unified theory of particle physics within the context of Heterotic M-Theory. It is demonstrated that there is always a region of moduli space where a bulk space five-brane is wrapped on a pure fiber in the Calabi-Yau threefold. Restricting the discussion to the smooth parts of the discriminant curve, we explore the properties of the N = 2 BPS supermultiplets that arise on the worldvolume of this five-brane due to the degeneration of the elliptic fiber. The associated degenerating M membranes are shown to project to string junctions in the base space. We use string junction techniques to explicitly compute the light BPS hyper-and vector multiplet spectrum for each Kodaira type fiber near the smooth part of the discriminant curve in the SU (5) GUT theory.

Supersymmetric Galileons

“…It is encouraging to see that healthy supersymmetric extensions of the Galileon Lagrangians exist, as demonstrated above. We would like to emphasize once more that, as should be clear already from the discussion around (78), the supersymmetric extension of L 4 given above is not unique. Hence it would be interesting to see, should a derivation of a supersymmetric Galileon theory be found in a more fundamental setting, precisely which form of the Lagrangian would arise.…”

“…When we supersymmetrize these theories, we use the same form for L 2 and L 3 , but for L 4 we use instead the last line in (78), and, for the reasons described before, we do not supersymmetrize L 5 explicitly. We then obtain…”

Lectures on Heterotic M-Theory

“…Then, it was shown in [49] that, in addition to the usual states, the I 2 degeneracy of the elliptic fiber produces an SU(2) doublet 2 of massless N = 2 hypermultiplets with unit electric charge. In general, one gets a complicated spectrum of new hypermultiplets and, for sufficiently intricate Kodaira singularities, new non-Abelian vector multiplets as well.…”

An abundance of heterotic vacua

“…A considerable amount of work has been devoted to developing techniques for constructing vector bundles and computing the associated cohomology groups [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”