188 research outputs found
-Algebras, the BV Formalism, and Classical Fields
We summarise some of our recent works on -algebras and quasi-groups
with regard to higher principal bundles and their applications in twistor
theory and gauge theory. In particular, after a lightning review of
-algebras, we discuss their Maurer-Cartan theory and explain that any
classical field theory admitting an action can be reformulated in this context
with the help of the Batalin-Vilkovisky formalism. As examples, we explore
higher Chern-Simons theory and Yang-Mills theory. We also explain how these
ideas can be combined with those of twistor theory to formulate maximally
superconformal gauge theories in four and six dimensions by means of
-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
Quantization of Flag Manifolds and their Supersymmetric Extensions
We first review the description of flag manifolds in terms of Pluecker coordinates and coherent states. Using this description, we construct fuzzy versions of the algebra of functions on these spaces in both operatorial and star product language. Our main focus is here on flag manifolds appearing in the double fibration underlying the most common twistor correspondences. After extending the Pluecker description to certain supersymmetric cases, we also obtain the appropriate deformed algebra of functions on a number of fuzzy flag supermanifolds. In particular, fuzzy versions of Calabi-Yau supermanifolds are found
'Schwinger Model' on the Fuzzy Sphere
In this paper, we construct a model of spinor fields interacting with
specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this
'Schwinger model'. In constructing the theory of gauge fields interacting with
spinors on fuzzy sphere, we take the approach that the Dirac operator on
q-deformed fuzzy sphere is the gauged Dirac operator on fuzzy
sphere. This introduces interaction between spinors and specific one parameter
family of gauge fields. We also show how to express the field strength for this
gauge field in terms of the Dirac operators and alone. Using the path
integral method, we have calculated the point functions of this model and
show that, in general, they do not vanish, reflecting the chiral non-invariance
of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys.
Lett.
Super Calabi-Yau's and Special Lagrangians
We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and
show that the mirror can be recast in a form which depends only on the
superdimension and which is reminiscent of a generalized conifold. We discuss
its geometrical properties in comparison to the familiar conifold geometry. In
the second part of the paper examples of special-Lagrangian submanifolds are
constructed for a class of super Calabi-Yau's. We finally comment on their
infinitesimal deformations.Comment: 20 pages, no figures, latex; v2: references added; v3: minor
clarifications added, version published in JHE
Towards an M5-Brane Model II:Metric String Structures
In this paper, we develop the mathematical formulation of metric string
structures. These play a crucial role in the formulation of certain
six-dimensional superconformal field theories and we believe that they also
underlie potential future formulations of the (2,0)-theory. We show that the
connections on non-abelian gerbes usually introduced in the literature are
problematic in that they are locally gauge equivalent to connections on abelian
gerbes. Connections on string structures form an exception and we introduce the
general concept of an adjusted Weil algebra leading to potentially interacting
connections on higher principal bundles. Considering a special case, we derive
the metric extension of string structures and the corresponding adjusted Weil
algebra. The latter lead to connections that were previously constructed by
hand in the context of gauged supergravities. We also explain how the Leibniz
algebras induced by an embedding tensor in gauged supergravities fit into our
picture.Comment: v2: 70 pages, presentation improved, typos fixed, published versio
Quantization of Magnetic Poisson Structures:LMS/EPSRC Durham Symposium on Higher Structures in M-Theory
We describe three perspectives on higher quantization, using the example of
magnetic Poisson structures which embody recent discussions of nonassociativity
in quantum mechanics with magnetic monopoles and string theory with
non-geometric fluxes. We survey approaches based on deformation quantization of
twisted Poisson structures, symplectic realization of almost symplectic
structures, and geometric quantization using 2-Hilbert spaces of sections of
suitable bundle gerbes. We compare and contrast these perspectives, describing
their advantages and shortcomings in each case, and mention many open avenues
for investigation.Comment: 13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
Matrix Models and D-branes in Twistor String Theory
We construct two matrix models from twistor string theory: one by dimensional
reduction onto a rational curve and another one by introducing noncommutative
coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment
on the interpretation of our matrix models in terms of topological D-branes and
relate them to a recently proposed string field theory. By extending one of the
models, we can carry over all the ingredients of the super ADHM construction to
a D-brane configuration in the supertwistor space P^(3|4). Eventually, we
present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio
Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
We extend the analysis of hep-th/0408069 on a Lorentz invariant
interpretation of noncommutative spacetime to field theories on
non-anticommutative superspace with half the supersymmetries broken. By
defining a Drinfeld-twisted Hopf superalgebra, it is shown that one can restore
twisted supersymmetry and therefore obtain a twisted version of the chiral
rings along with certain Ward-Takahashi identities. Moreover, we argue that the
representation content of theories on the deformed superspace is identical to
that of their undeformed cousins and comment on the consequences of our
analysis concerning non-renormalization theorems.Comment: 1+17 pages; typos fixed, minor correction
Fuzzy Scalar Field Theory as a Multitrace Matrix Model
We develop an analytical approach to scalar field theory on the fuzzy sphere
based on considering a perturbative expansion of the kinetic term. This
expansion allows us to integrate out the angular degrees of freedom in the
hermitian matrices encoding the scalar field. The remaining model depends only
on the eigenvalues of the matrices and corresponds to a multitrace hermitian
matrix model. Such a model can be solved by standard techniques as e.g. the
saddle-point approximation. We evaluate the perturbative expansion up to second
order and present the one-cut solution of the saddle-point approximation in the
large N limit. We apply our approach to a model which has been proposed as an
appropriate regularization of scalar field theory on the plane within the
framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement
Gauge symmetries of strings in supertwistor space
Recently we have considered supertwistor reformulation of the D=4 N=1,2
superstring action that comprises Newman-Penrose dyad components and is
classically equivalent to the Green-Schwarz one. It was shown that in the
covariant kappa-symmetry gauge the supertwistor representation of the string
action simplifies. Here we analyze its Hamiltonian formulation, classify the
constraints on the phase-space variables, and find the covariant set of
generators of the gauge symmetries. Quantum symmetries of the supertwistor
representation of the string action are examined applying the world-sheet CFT
technique. Considered are various generalizations of the model from the
perspective of their possible relation to known twistor superstring models.Comment: 17 pages, LaTeX; v.2 minor changes in the text, references added,
misprints correcte
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