## Thursday, March 15, 2007 ... //

### Connecting supercritical string theories with others

My day has been kind of long so this report will be somewhat short.

Simeon Hellerman gave a very interesting talk about the connections between different string theories and a spontaneous disappearance of spacetime dimensions, based mostly on his work with Ian Swanson and other papers of Simeon.

The main idea is that you can create cosmological solutions in perturbative supercritical or critical string theory where two regions A,B (here, A will be a higher-dimensional vacuum and B will be a lower-dimensional vacuum) are separated by a wall that resembles the Liouville wall but moves by the speed of light.

The wall is in the X0-X1 plane that is equipped with a time-like linear dilaton (necessary to get the right central charge in a supercritical theory) and a light-like exponentially growing tachyon (which is on-shell due to the extra coupling with the dilaton gradient). There is another dimension X2 and we turn on some additional tachyon whose profile goes like "X2^2" times a coefficient that depends on the X0-X1 coordinates. The effect of this term is that the region B only allows string states whose zero modes are described by a harmonic oscillator ground state and that have no non-trivial Fourier oscillator excitations either to enter.

In this sense, the region B is filled with a tachyon that prevents all excitations from entering the region except for excitations that pretend that one dimension of space doesn't exist. Using similar configurations and marginal perturbations of the worldsheet CFT, they can connect or interpolate different pairs of theories with tachyons such as type 0 theories in different dimensions, bosonic strings in different dimensions with various but different diagonal current algebras, as well as type 0 on an orbifold with type II in lower dimensions (the additional chiral GSO projection arises from the orbifold projection).

The most non-trivial connection is one between the bosonic string and the type 0 string. It uses the Berkovits-Vafa old relation between CFTs with different worldsheet supersymmetry: