Phenomenology of codimension-2 brane worlds: the importance of back-reaction

Abstract

<p>In this thesis, we describe the properties of brane worlds embedded in a spacetime with two extra dimensions. We derive and describe the boundary conditions that branes impose on the bulk fields in the theory, and show that they reproduce known results for D7 branes in F-theory compactifications of type IIB supergravity. We show how brane-bulk couplings can stabilize moduli of a flux stabilized compactification of extra dimensions. An important new ingredient is that the branes can have a magnetic coupling to the flux that stabilizes the bulk. This coupling allows the system to relax the stringent constraints of flux quantization, which allows the bulk spacetime to respond to perturbations of the branes. We derive the dynamics of the lower-dimensional effective theory below the Kaluza-Klein scale, and show that the contributions of the magnetic coupling can be competitive with the tension of the brane. We first describe the simplest flux compactification: an Einstein-scalar- Maxwell theory in 6 dimensions. We find that the effective potential in 4 dimensions gets minimized at the position one would naively expect - at the stationary point of the sum of all the brane Lagrangians - but its value at the minimum gets changed by the magnetic coupling to the brane. Next we find that if the bulk is described by 6 dimensional gauged chiral supergravity, the effect of the magnetic coupling allows the curvature on the brane to be suppressed relative to the generic scale of the tension on the branes. We use this observation to construct an explicit brane-bulk system that has a technically natural cosmological constant of the correct size. The classical on-brane curvature vanishes in our construction, and the first order quantum corrections give a value to the cosmological constant of the right order of magnitude. We estimate higher loop corrections, and they are greatly suppressed.</p>