1. 1 Research supported by the National Science Foundation grant PHY-0757959. Opinions expressed are those of the authors and do not necessarily reflect the views of NSF. Esse est percipi TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AAAAA A AAAA A A AAA A AA A

2. 2 Superstring Amplitudes as a Mellin Transform of Supergravity Tomasz Taylor Northeastern University, Boston Based on work with Stephan Stieberger (MPI, Munich) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AAA A A

3. 3 Superstring Amplitudes as a Mellin Transform of Supergravity TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AAA A A Do not confuse with KLT !

4. 4 Superstring Example: N=4 (Veneziano-Virasoro) four-gluon amplitude

5. 5 Superstring All N MHV formula (Stieberger, Taylor, 2012, and a general formula of Mafra, Schlotterer, Stieberger, 2011)

6. 6 Superstring Supergravity (Mason, Skinner, 2010; Berends, Giele, Kuijf, 1988, Bern, Dixon, Perelstein, Rozowsky, 1999, Nguyen, Spradlin, Volovich, Wen, 2010,…) Very “Similar”

7. 7 Graphs for superstrings (and supergravity)

8. 8 Unified description: Hodges determinant Laplacian Matrix (Feng, He, 2012; based on Hodges, 2012)

9. Mellin Transform 9 From Koba-Nielsen to constraints

10. Pascal’s Triangles of Constraints 10

11. Summary: Superstring /Supergravity Correspondence Superstring Amplitudes are Mellin Transforms of Supergravity, directly from the worlsheet into the dual space of kinematic invariants, thus bypassing space-time… 11

12. In retrospective, this is not totally unexpected: Inverse (multiple) Mellin transforms of hypergeometric string “formfactors” are simple delta functions localizing on the world- sheet. Very similar to SYM amplitudes in twistor string or Grassmanian formulations. Mellin “trivialize” string amplitudes 12

13. To be done Proof of Superstring/Supergravity correspondence for all tree- level amplitudes, beyond MHV (in progress) Mellin transforms are not completely trivial because the integrations are over a constrained surface (Pascal’s triangle). Understanding the nature of this embedding will allow a deeper understanding of the correspondence and to establish a supergravity description of “stringy” features: Regge resonance poles etc. For the moment, we can say that Superstring Theory is Supergravity in a Brilliant Disguise (Bruce Springsteen, 1987) 13

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