31,104 research outputs found
Doubled \alpha'-Geometry
We develop doubled-coordinate field theory to determine the \alpha'
corrections to the massless sector of oriented bosonic closed string theory.
Our key tool is a string current algebra of free left-handed bosons that makes
O(D,D) T-duality manifest. While T-dualities are unchanged, diffeomorphisms and
b-field gauge transformations receive corrections, with a gauge algebra given
by an \alpha'-deformation of the duality-covariantized Courant bracket. The
action is cubic in a double metric field, an unconstrained extension of the
generalized metric that encodes the gravitational fields. Our approach provides
a consistent truncation of string theory to massless fields with corrections
that close at finite order in \alpha'.Comment: 54 pages, v2: version published in JHE
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
We study higher form Proca equations on Einstein manifolds with boundary data
along conformal infinity. We solve these Laplace-type boundary problems
formally, and to all orders, by constructing an operator which projects
arbitrary forms to solutions. We also develop a product formula for solving
these asymptotic problems in general. The central tools of our approach are (i)
the conformal geometry of differential forms and the associated exterior
tractor calculus, and (ii) a generalised notion of scale which encodes the
connection between the underlying geometry and its boundary. The latter also
controls the breaking of conformal invariance in a very strict way by coupling
conformally invariant equations to the scale tractor associated with the
generalised scale. From this, we obtain a map from existing solutions to new
ones that exchanges Dirichlet and Neumann boundary conditions. Together, the
scale tractor and exterior structure extend the solution generating algebra of
[31] to a conformally invariant, Poincare--Einstein calculus on (tractor)
differential forms. This calculus leads to explicit holographic formulae for
all the higher order conformal operators on weighted differential forms,
differential complexes, and Q-operators of [9]. This complements the results of
Aubry and Guillarmou [3] where associated conformal harmonic spaces parametrise
smooth solutions.Comment: 85 pages, LaTeX, typos corrected, references added, to appear in
Memoirs of the AM
Phase boundaries in algebraic conformal QFT
We study the structure of local algebras in relativistic conformal quantum
field theory with phase boundaries. Phase boundaries are instances of a more
general notion of boundaries that give rise to a variety of algebraic
structures. These can be formulated in a common framework originating in
Algebraic QFT, with the principle of Einstein Causality playing a prominent
role.We classify the phase boundary conditions by the centre of a certain
universal construction, which produces a reducible representation in which all
possible boundary conditions are realized. For a large class of models, the
classification reproduces results obtained in a different approach by Fuchs et
al. before.Comment: 40 pages, v3: several corrections, matches published versio
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
The Superconformal Xing Equation
Crossing symmetry provides a powerful tool to access the non-perturbative
dynamics of conformal and superconformal field theories. Here we develop the
mathematical formalism that allows to construct the crossing equations for
arbitrary four-point functions in theories with superconformal symmetry of type
I, including all superconformal field theories in dimensions. Our advance
relies on a supergroup theoretic construction of tensor structures that
generalizes an approach which was put forward in \cite{Buric:2019dfk} for
bosonic theories. When combined with our recent construction of the relevant
superblocks, we are able to derive the crossing symmetry constraint in
particular for four-point functions of arbitrary long multiplets in all
4-dimensional superconformal field theories.Comment: 49 page
Weaving Worldsheet Supermultiplets from the Worldlines Within
Using the fact that every worldsheet is ruled by two (light-cone) copies of
worldlines, the recent classification of off-shell supermultiplets of
N-extended worldline supersymmetry is extended to construct standard off-shell
and also unidextrous (on the half-shell) supermultiplets of worldsheet
(p,q)-supersymmetry with no central extension. In the process, a new class of
error-correcting (even-split doubly-even linear block) codes is introduced and
classified for , providing a graphical method for classification of
such codes and supermultiplets. This also classifies quotients by such codes,
of which many are not tensor products of worldline factors. Also,
supermultiplets that admit a complex structure are found to be depictable by
graphs that have a hallmark twisted reflection symmetry.Comment: Extended version, with added discussion of complex and quaternionic
tensor products demonstrating that certain quotient supermultiplets do not
factorize over any ground fiel
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