Seminar Announcement Date for the seminar : 2nd February Time : 11.30 AM Venue: Lecture Hall 6 Constraining treelevel gravitational scattering Subham Dutta Chowdhury University of Chicago. 020223 Abstract We study the space of all kinematically allowed four graviton Smatrices, having simple poles and polynomial in scattering momenta. To classify pole exchanges, we enumerate all possible three point couplings involving two gravitons and a massive spinning particle transforming in an irreducible representation of the lorentz group. We demonstrate that the space of analytic (i.e polynomial in momenta unlike pole exchanges) Smatrices is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these cubic couplings and modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four graviton Smatrix at any given derivative order. We also explicitly list the cubic and quartic local Lagrangians that give rise to these Smatrices. We then conjecture that the Regge growth of Smatrices in all physically acceptable classical theories is bounded by s^2 at fixed t (Class ical Regge Growth conjecture). Using flat space limit of AdS correlators and Chaos bound, we prove CRG in the context of a certain class of interactions. We then use CRG to rule out modifications to Einstein gravity no polynomial addition to the Einstein Smatrix obeys this bound for D\leq 6. For D\geq7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton Smatrix does not admit any physically acceptable polynomial modifications for D\leq 6. We also show that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth.
