Seminar series
Date
Mon, 10 Nov 2014
Time
12:00 -
13:00
Location
L5
Speaker
Tomasz Lukowski
Organisation
Oxford
In this talk I will discuss how to construct all solutions consistent with crossing symmetry in the limit of large central charge $c ~ N^2$, starting from the four-point correlator of the stress tensor multiplet in N=4 SYM. Unitarity forces the introduction of a scale $\Delta_{gap}$ and these solutions organize as a double expansion in 1/c and $1/\Delta_{gap}$. These solutions are valid to leading order in 1/c and to all orders in $1/\Delta_{gap}$ and reproduce, in particular, instanton corrections previously found. Comparison with such instanton computations allows to fix $\Delta_{gap}$. Using this gap scale one can explain the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. Furthermore, I will present connections between such upper bounds and positivity constraints arising from causality in flat space and I will discuss how certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.