## Friday, November 18, 2005

Melanie Becker organizes nice lectures at the Radcliffe Institute, formerly known as Harvard University for girls. The first lecture was by Cumrun Vafa - about the Swampland, and two talks by Nima Arkani-Hamed followed. Today, he described our project (with Cumrun Vafa, me, and Alberto Nicolis) involving the "weak gravity" constraints. In my opinion, he did a terrific job. Let me only summarize a few slogans:

• in quantum gravity i.e. string theory, one should have no global continuous symmetries; it is known in string theory that a symmetry current, a (1,0) or (0,1) tensor, is associated with any symmetry, and it can be multiplied by "del X" or "delBAR X" to create a (1,1) marginal vertex operator for a gauge boson, proving that the symmetry is local after all
• this constraint looks too fragile because one can immitate global symmetries by weak symmetries with a very small coupling constant which seem allowed
• therefore, it would be more natural if very weak couplings were forbidden, too
• more precisely, if a U(1) gauge group has too small a coupling, ...

This posting was never finished. Read the preprint hep-th/0601001.