New massive "dark" vector bosons are ubiquitous in BSM physics. I'll discuss the effective theories, interactions, and applications of theories with a (single) massive vector boson with a Stückelberg mass, with the goal of providing a clear and self-consistent approach to the (sometimes confusing) subject. The critical role of possible couplings of the longitudinal mode will be emphasized, demarcating when theories have amplitudes that grow with energy. In such theories, I'll identify the cutoff scale, as well as show the potential of longitudinally-enhanced observables given specific couplings of the vector boson. The Stückelbergian approach to massive vectors also provides insight into generalized dark vector boson theories; I'll demonstrate a specific application to an "electrophobic" vector field that can evade many terrestrial experiment constraints that would otherwise apply to a dark photon.
3d mirror symmetry predicts an equivalence between A- and B-twists of a pair of dual 3d N=4 theories. Essentially the strongest invariants one can produce of the resulting 3-dimensional topological field theories are their 2-categories of boundary conditions. The B-side 2-category was first described by Kapustin-Rozansky-Saulinas, but the 2-categorical structure on A-side boundary conditions has not previously been understood. For abelian gauge theories with matter, we propose a model for the 2-category of A-type boundary conditions using Kapranov-Schechtman's "perverse schobers," and we prove a 3d mirror equivalence between dual 2-categories. By reducing to lower-dimensions, we can recover both the BFN construction and the BLPW Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.
I will continue the discussions on line defects and surface defects in class S theories, making connections to the construction of the quantum trace map, as well as to the exact WKB method for higher order ODEs.
Inflation can be viewed as a natural "cosmological particle detector" which can probe energies as high as its Hubble scale. In this talk, I study the imprints of heavy relativistic particles during inflation on primordial correlators in situations where the scalar fluctuations have a reduced speed of sound. Breaking dS boosts allows new types of footprints of massive fields to emerge. In particular, I show that heavy particles that are lighter than Hubble divided by the speed of sound leave smoking gun imprints in the three-point function of curvature perturbations (due to the exchange of those fields) in the form of resonances in the squeezed limit which are vividly distinct from the previously explored signatures of heavy fields in de Sitter correlators. Throughout I use and extend the cosmological bootstrap techniques derived from locality, unitarity, and analyticity in order to find fully analytical formulae for the desired boost breaking correlators.
In the first part of my talk I'll briefly review some aspects of the relations
between N=4, d=4 SYM and vertex operator algebras (VOAs) discussed
in recent work of Gaiotto and collaborators. The resulting picture predicts
conjectural generalisations of the geometric Langlands correspondence.
We will focus on a class of examples figuring prominently in recent work
of Creutzig-Dimofte-Garner-Geer, labelled by parameters n (rank) and k.
For the case k=1,n=2 we will point out that the conformal blocks of the
relevant VOA, twisted by local systems, represent sections of natural
holomorphic line bundles over the moduli spaces of local systems closely
related to the isomonodromic tau functions. Observing the crucial role of
(quantised) cluster algebras in the definition of the holomorphic line
bundles suggests natural generalisations of this story to higher values
of the parameters k and n.