Codimension-2 brane–bulk matching: examples from six and ten dimensions

Experience with Randall–Sundrum models teaches the importance of following how branes back-react onto the bulk geometry, since this can dramatically affect the system's low-energy properties. Yet the practical use of this observation for model building is so far mostly restricted to branes having only one transverse dimension (codimension-1) in the bulk space, since this is where tools for following back-reaction are well developed. This is likely to be a serious limitation since experience also tells us that one dimension is rarely representative of what happens in higher dimensions. Here we summarize recent progress in developing the matching conditions that describe how codimension-2 branes couple to bulk metric, gauge and scalar fields. These matching conditions are then applied to three situations: D7-branes in F-theory compactifications of ten-dimensional (10D) Type IIB string vacua; 3-branes coupled to bulk axions in unwarped and non-supersymmetric six-dimensional (6D) systems; and 3-branes coupled to chiral, gauged 6D supergravity. For each it is shown how the resulting brane–bulk dynamics are reproduced by the scalar potential for the low-energy moduli in the dimensionally reduced, on-brane effective theory. For 6D supergravity, we show that the only 4D-maximally symmetric bulk geometries supported by positive-tension branes are flat.