211 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
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
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
'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.
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
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
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
N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2
We study D-branes in the background of Euclidean AdS2xS2 with a graviphoton
field turned on. As the background is not Ricci flat, the graviphoton field
must have both self-dual and antiself-dual parts. This, in general, will break
all the supersymmetries on the brane. However, we show that there exists a
limit for which one can restore half of the supersymmetries. Further, we show
that in this limit, the N=1/2 SYM Lagrangian on flat space can be lifted on to
the Euclidean AdS2xS2 preserving the same amount of supersymmetries as in the
flat case. We observe that without the C-dependent terms present in the action
this lift is not possible.Comment: 12 pages, latex file; v2: minor corrections, references adde
Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction
We study an extension of the ADHM construction to give deformed
anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n)
gauge group. First we extend the exterior algebra on superspace to
non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory
can be reformulated in a geometrical way. By using this exterior algebra, we
formulate a non(anti)commutative version of the super ADHM construction and
show that the curvature two-form superfields obtained by our construction do
satisfy the deformed ASD equations and thus we establish the deformed super
ADHM construction. We also show that the known deformed U(2) one instanton
solution is obtained by this construction.Comment: 32 pages, LaTeX, v2: typos corrected, references adde
Deformation of Super Yang-Mills Theories in R-R 3-form Background
We study deformation of N=2 and N=4 super Yang-Mills theories, which are
obtained as the low-energy effective theories on the (fractional) D3-branes in
the presence of constant Ramond-Ramond 3-form background. We calculate the
Lagrangian at the second order in the deformation parameter from open string
disk amplitudes. In N=4 case we find that all supersymmetries are broken for
generic deformation parameter but part of supersymmetries are unbroken for
special case. We also find that classical vacua admit fuzzy sphere
configuration. In N=2 case we determine the deformed supersymmetries. We
rewrite the deformed Lagrangians in terms of N=1 superspace, where the
deformation is interpreted as that of coupling constants.Comment: v2: reference added, v3: published version in JHE
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