Pedro Vieira

My current main research aims at developing new techniques for studying quantum field theories and string theories at finite coupling. To do so, I am pursuing two very distinct complementary directions. On the on one hand I am studying a very special massless supersymmetric quantum field theory known as N=4 SYM. This theory is a formidable toy theory. It is simple enough that we can hope to solve it completely while sufficiently rich that we can hope to extract deep lessons about the foundations of quantum field theory and string theory from its solution. The main tools in this program are a combination of non-perturbative tools known as Integrability combined with holographic ideas. On the other hand, I am trying to understand the space of all quantum field theories. Here, rather than solving in full analytic detail a quantum field theory we are trying to carve out the space of theories by asking more general questions such as what are the possible couplings and parameters of quantum field theories given a non-perturbative mass spectrum, symmetries etc. Here we are exploring various Bootstrap ideas, be it the conformal bootstrap program, the S-matrix bootstrap and even the Integrable bootstrap.