54 research outputs found
Induced Action for Conformal Higher Spins from Worldline Path Integrals
Conformal higher spin (CHS) fields, despite being non unitary, provide a
remarkable example of a consistent interacting higher spin theory in flat space
background, that is local to all orders. The non-linear action is defined as
the logarithmically UV divergent part of a one-loop scalar effective action. In
this paper we take a particle model, that describes the interaction of a scalar
particle to the CHS background, and compute its path integral on the circle. We
thus provide a worldline representation for the CHS action, and rederive its
quadratic part. We plan to come back to the subject, to compute cubic and
higher vertices, in a future work.Comment: 24 pages, references added, minor typos correcte
Leibniz Gauge Theories and Infinity Structures
We formulate gauge theories based on Leibniz(-Loday) algebras and uncover
their underlying mathematical structure. Various special cases have been
developed in the context of gauged supergravity and exceptional field theory.
These are based on `tensor hierarchies', which describe towers of -form
gauge fields transforming under non-abelian gauge symmetries and which have
been constructed up to low levels. Here we define `infinity-enhanced Leibniz
algebras' that guarantee the existence of consistent tensor hierarchies to
arbitrary level. We contrast these algebras with strongly homotopy Lie algebras
( algebras), which can be used to define topological field theories
for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries
an associated algebra, which we discuss.Comment: 50 pages, v2: refs added, new subsection 3.2, version to appear in
Comm. Math. Phy
Particles with non abelian charges
Efficient methods for describing non abelian charges in worldline approaches
to QFT are useful to simplify calculations and address structural properties,
as for example color/kinematics relations. Here we analyze in detail a method
for treating arbitrary non abelian charges. We use Grassmann variables to take
into account color degrees of freedom, which however are known to produce
reducible representations of the color group. Then we couple them to a U(1)
gauge field defined on the worldline, together with a Chern-Simons term, to
achieve projection on an irreducible representation. Upon gauge fixing there
remains a modulus, an angle parametrizing the U(1) Wilson loop, whose
dependence is taken into account exactly in the propagator of the Grassmann
variables. We test the method in simple examples, the scalar and spin 1/2
contribution to the gluon self energy, and suggest that it might simplify the
analysis of more involved amplitudes.Comment: 14 page
Mode Regularization for N=1,2 SUSY Sigma Model
Worldline N=1 and N=2 supersymmetric sigma models in curved background are
useful to describe spin one-half and spin one particles coupled to external
gravity, respectively. It is well known that worldline path integrals in curved
space require regularization: we present here the mode-regularization for these
models, finding in particular the corresponding counterterms, both in the case
of flat and curved indices for worldline fermions. For N=1, using curved
indices we find a contribution to the counterterm from the fermions that
cancels the contribution of the bosons, leading to a vanishing total
counterterm and thus preserving the covariance and supersymmetry of the
classical action. Conversely in the case of N=2 supersymmetries we obtain a
non-covariant counterterm with both curved and flat indices. This work
completes the analysis of the known regularization schemes for N=1,2 nonlinear
sigma models in one dimension.Comment: 15 page
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