146 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
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
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
Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
We propose a deformation of SYM theoery induced by
nonanticommutative star product. The deformation introduces new bosonic terms
which we identify with the corresponding Myers terms of a stack of D3-branes in
the presence of a five-form RR flux. We take this as an indication that the
deformed lagrangian describes D3-branes in such a background. The vacuum states
of the theory are also examined. In a specific case where the U(1) part of the
gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the
brane sit on a fuzzy two sphere. For a supersymmetric vacuum the
antiholomorphic coordinates must necessarily commute. However, we also
encounter non-supersymmetric vacua for which the antiholomorphic coordinates do
not commute.Comment: 14 pages, minor changes, refs. adde
The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
In the recent paper hep-th/0502076, it was argued that the open topological
B-model whose target space is a complex (2|4)-dimensional mini-supertwistor
space with D3- and D1-branes added corresponds to a super Yang-Mills theory in
three dimensions. Without the D1-branes, this topological B-model is equivalent
to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the
latter with a holomorphic BF-type theory, we describe a twistor correspondence
between this theory and a supersymmetric Bogomolny model on R^3. The connecting
link in this correspondence is a partially holomorphic Chern-Simons theory on a
Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the
mini-supertwistor space. Along the way of proving this twistor correspondence,
we review the necessary basic geometric notions and construct action
functionals for the involved theories. Furthermore, we discuss the geometric
aspect of a recently proposed deformation of the mini-supertwistor space, which
gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually,
we present solution generating techniques based on the developed twistorial
description together with some examples and comment briefly on a twistor
correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio
Vortex-line liquid phases: Longitudinal superconductivity in the lattice London model
We study the vortex-line lattice and liquid phases of a clean type-II
superconductor by means of Monte Carlo simulations of the lattice London model.
Motivated by a recent controversy regarding the presence, within this model, of
a vortex-liquid regime with longitudinal superconducting coherence over long
length scales, we directly compare two different ways to calculate the
longitudinal coherence. For an isotropic superconductor, we interpret our
results in terms of a temperature regime within the liquid phase in which
longitudinal superconducting coherence extends over length scales larger than
the system thickness studied. We note that this regime disappears in the
moderately anisotropic case due to a proliferation, close to the flux-line
lattice melting temperature, of vortex loops between the layers.Comment: 8 pages, Revtex, with eps figures. To appear in Phys. Rev.
Vertex Operators for Closed Superstrings
We construct an iterative procedure to compute the vertex operators of the
closed superstring in the covariant formalism given a solution of IIA/IIB
supergravity. The manifest supersymmetry allows us to construct vertex
operators for any generic background in presence of Ramond-Ramond (RR) fields.
We extend the procedure to all massive states of open and closed superstrings
and we identify two new nilpotent charges which are used to impose the gauge
fixing on the physical states. We solve iteratively the equations of the vertex
for linear x-dependent RR field strengths. This vertex plays a role in studying
non-constant C-deformations of superspace. Finally, we construct an action for
the free massless sector of closed strings, and we propose a form for the
kinetic term for closed string field theory in the pure spinor formalism.Comment: TeX, harvmac, amssym.tex, 41 pp; references adde
Symmetry, Gravity and Noncommutativity
We review some aspects of the implementation of spacetime symmetries in
noncommutative field theories, emphasizing their origin in string theory and
how they may be used to construct theories of gravitation. The geometry of
canonical noncommutative gauge transformations is analysed in detail and it is
shown how noncommutative Yang-Mills theory can be related to a gravity theory.
The construction of twisted spacetime symmetries and their role in constructing
a noncommutative extension of general relativity is described. We also analyse
certain generic features of noncommutative gauge theories on D-branes in curved
spaces, treating several explicit examples of superstring backgrounds.Comment: 52 pages; Invited review article to be published in Classical and
Quantum Gravity; v2: references adde
The ‘microflora hypothesis’ of allergic diseases
Increasingly, epidemiologic and clinical data support the hypothesis that perturbations in the gastrointestinal (GI) microbiota because of antibiotic use and dietary differences in ‘industrialized’ countries have disrupted the normal microbiota-mediated mechanisms of immunological tolerance in the mucosa, leading to an increase in the incidence of allergic airway disease. The data supporting this ‘microflora hypothesis’ includes correlations between allergic airway disease and (1) antibiotic use early in life, (2) altered fecal microbiota and (3) dietary changes over the past two decades. Our laboratory has recently demonstrated that mice can develop allergic airway responses to allergens if their endogenous microbiota is altered at the time of first allergen exposure. These experimental and clinical observations are consistent with other studies demonstrating that the endogenous microbiota plays a significant role in shaping the development of the immune system. Data are beginning to accumulate that a ‘balanced’ microbiota plays a positive role in maintaining mucosal immunologic tolerance long after post-natal development. Other studies have demonstrated that even small volumes delivered to the nasopharynx largely end up in the GI tract, suggesting that airway tolerance and oral tolerance may operate simultaneously. The mechanism of microbiota modulation of host immunity is not known; however, host and microbial oxylipins are one potential set of immunomodulatory molecules that may control mucosal tolerance. The cumulative data are beginning to support the notion that probiotic and prebiotic strategies be considered for patients coming off of antibiotic therapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73451/1/j.1365-2222.2005.02379.x.pd
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