2 research outputs found
A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
Boundaries in gauge theories are a delicate issue. Arbitrary boundary choices
enter the calculation of charges via Noether's second theorem, obstructing the
assignment of unambiguous physical charges to local gauge symmetries. Replacing
the arbitrary boundary choice with new degrees of freedom suggests itself. But,
concretely, such boundary degrees of freedom are spurious---i.e. they are not
part of the original field content of the theory---and have to disappear upon
gluing. How should we fit them into what we know about field-theory? We resolve
these issues in a unified and geometric manner, by introducing a connection
1-form, , in the field-space of Yang-Mills theory. Using this geometric
tool, a modified version of symplectic geometry---here called `horizontal'---is
possible. Independently of boundary conditions, this formalism bestows to each
region a physical notion of charge: the horizontal Noether charge. The
horizontal gauge charges always vanish, while global charges still arise for
reducible configurations characterized by global symmetries. The field-content
itself is used as a reference frame to distinguish `gauge' and `physical'; no
new degrees of freedom, such as group-valued edge modes, are required.
Different choices of reference fields give different 's, which are
cousins of gauge-fixing like the Higgs-unitary and Coulomb gauges. But the
formalism extends well beyond gauge-fixings, for instance by avoiding the
Gribov problem. For one choice of , would-be Goldstone modes arising
from the condensation of matter degrees of freedom play precisely the role of
the known group-valued edge modes, but here they arise as preferred coordinates
in field space, rather than new fields. For another choice, in the Abelian
case, recovers the Dirac dressing of the electron.Comment: 71 pages, 3 appendices, 9 figures. Summary of the results at the
beginning of the paper. v2: numerous improvements in the presentation, and
introduction of new references, taking colleague feedback into accoun
Scalar Asymptotic Charges and Dual Large Gauge Transformations
In recent years soft factorization theorems in scattering amplitudes have
been reinterpreted as conservation laws of asymptotic charges. In gauge,
gravity, and higher spin theories the asymptotic charges can be understood as
canonical generators of large gauge symmetries. Such a symmetry interpretation
has been so far missing for scalar soft theorems. We remedy this situation by
treating the massless scalar field in terms of a dual two-form gauge field. We
show that the asymptotic charges associated to the scalar soft theorem can be
understood as generators of large gauge transformations of the dual two-form
field.
The dual picture introduces two new puzzles: the charges have very unexpected
Poisson brackets with the fields, and the monopole term does not always have a
dual gauge transformation interpretation. We find analogs of these two
properties in the Kramers-Wannier duality on a finite lattice, indicating that
the free scalar theory has new edge modes at infinity that canonically commute
with all the bulk degrees of freedom.Comment: 16 pages, 2 figure