IAS High Energy Theory Seminar
We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. This gives a complete description of open-closed string field theory in the topological B-model. We explain an anomaly cancellation mechanism at all loops in perturbation theory in this model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. This is joint work with Kevin Costello.
We analyze modular invariance drawing inspiration from tauberian
theorems. Given a modular invariant partition function with a positive
spectral density, we derive lower and upper bounds on the number of
operators within a given energy interval. They are most revealing at high
energies. In this limit we rigorously derive the Cardy formula for the
microcanonical entropy together with optimal error estimates for various
widths of the averaging energy shell. Finally, we identify a new universal
I will discuss time-dependent probes of the renormalization group, and derive new constraints that govern the spread of local operators in holographic theories. The same methods lead to sum rules for inflationary correlators, relating observables, like the speed of sound during inflation, to properties of the UV theory.
We present recent advances in constructions of globally consistent
F-theory compactifications with the exact chiral spectrum of the minimal
supersymmetric Standard Model. We highlight the first such example and
then turn to a subsequent systematic exploration of the landscape of
F-theory three-family Standard Models with a gauge coupling unification.
Employing algebraic geometry techniques, all global consistency
conditions of these models can be reduced to a single criterion on the
Anomalies are invariants under renormalization group flow which lead to powerful constraints on the phases of quantum field theories. I will explain how these ideas can be generalized to families of theories labelled by coupling constants like the theta angle in gauge theory. Using these ideas we will be able to prove that certain systems, such as Yang-Mills theory in 4d, necessarily have a phase transition as these parameters are varied. We will also show how to use the same ideas to constrain the dynamics of defects where coupling constants vary in spacetime.