344 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
Is Quantum Gravity a Chern-Simons Theory?
We propose a model of quantum gravity in arbitrary dimensions defined in
terms of the BV quantization of a supersymmetric, infinite dimensional matrix
model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the
space of observables of a quantum mechanical Hilbert space H. The model is
motivated by previous attempts to formulate gravity in terms of
non-commutative, phase space, field theories as well as the Fefferman-Graham
curved analog of Dirac spaces for conformally invariant wave equations. The
field equations are flat connection conditions amounting to zero curvature and
parallel conditions on operators acting on H. This matrix-type model may give a
better defined setting for a quantum gravity path integral. We demonstrate that
its underlying physics is a summation over Hamiltonians labeled by a conformal
class of metrics and thus a sum over causal structures. This gives in turn a
model summing over fluctuating metrics plus a tower of additional modes-we
speculate that these could yield improved UV behavior.Comment: 22 pages, LaTeX, 3 figures, references added, version to appear in
PR
Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras
It is postulated that quantum gravity is a sum over causal structures coupled
to matter via scale evolution. Quantized causal structures can be described by
studying simple matrix models where matrices are replaced by an algebra of
quantum mechanical observables. In particular, previous studies constructed
quantum gravity models by quantizing the moduli of Laplace, weight and
defining-function operators on Fefferman-Graham ambient spaces. The algebra of
these operators underlies conformal geometries. We extend those results to
include fermions by taking an osp(1|2) "Dirac square root" of these algebras.
The theory is a simple, Grassmann, two-matrix model. Its quantum action is a
Chern-Simons theory whose differential is a first-quantized, quantum mechanical
BRST operator. The theory is a basic ingredient for building fundamental
theories of physical observables.Comment: 4 pages, LaTe
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
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