Low-energy effective field theories arising from string compactificati — Andrew Strominger

"Why would there be math that had no physical manifestation?"

"The uncertainty principle of quantum mechanics says that all spacetime positions are slightly uncertain. ... Nothing is immune from the uncertainty principle. ... Applying the uncertainty principle to Einsteins , we find the rug of physics pulled from under our feet."

"We have no idea what science will look in, say, twenty or thirty years. ... Every scientist has to bet. Science is not a science — its an art and a gamble."

"The conditions for spacetime supersymmetry of the heterotic in backgrounds with arbitrary metric, torsion, Yang-Mills and dilaton expectation values are determined using the sigma model approach. The resulting equations are explicitly solved for the torsion and dilaton fields, and the remaining equations cast in a simple form. Previously unnoticed topological obstructions to solving these equations are found. The equations are shown to agree to leading order in perturbation theory with those derived in a field theory approach, provided one considers a more general ansatz than in previous analyses by allowing for a warp factor for the metric. Exact solutions with non-zero torsion are found, indicating a new class of finite sigma models."

"It is shown that many of the s of type II string theory and d = 11 supergravity can have boundaries on other p-branes. The rules for when this can and cannot occur are derived from charge conservation. For example it is found that membranes in d = 11 supergravity and IIA string theory can have boundaries on s. The boundary dynamics are governed by the self-dual d = 6 string. A collection of N parallel fivebranes contains 12N(N–1) self-dual strings which become tensionless as the fivebranes approach one another."

"Much of over the last century has concerned the reductionist quest to uncover the laws of nature at ever shorter distances. In the last decade it has become increasingly clear, from a variety of investigations, that this long march into the has neglected a surprising wealth of uncharted phenomena in the deep (IR). Far from being a boring place where all is trivial and well-understood, the deep IR in four-dimensional Minkowski space has a rich structure which we are only beginning to understand. Applications range from the IR divergence problem in , 𝒩=4 Yang-Mills and color memory in in black hole information and a possible fundamental new perspective on space, time and nature."