Complexity of Vacua and Near-Vacua

In this talk I will study the computational complexity of vacua and near-vacua in field theory and string theory. From analogy to protein folding, it is natural to expect that finding stable vacua is computationally hard, in the sense of complexity theory. However, I will demonstrate that this is the case even for metastable vacua. The problem is exacerbated in string theory, since setting up the hard problem of finding string vacua requires actually computing the scalar potential in a controlled regime. Such computations involve solving instances of computationally hard problems. Cosmological implications will be discussed in light of a recently proposed measure that utilizes computational complexity.