12,568 research outputs found
A note on the boundary contribution with bad deformation in gauge theory
Motivated by recently progresses in the study of BCFW recursion relation with
nonzero boundary contributions for theories with scalars and
fermions\cite{Bofeng}, in this short note we continue the study of boundary
contributions of gauge theory with the bad deformation. Unlike cases with
scalars or fermions, it is hard to use Feynman diagrams directly to obtain
boundary contributions, thus we propose another method based on the SYM theory. Using this method, we are able to write down a useful
on-shell recursion relation to calculate boundary contributions from related
theories. Our result shows the cut-constructibility of gauge theory even with
the bad deformation in some generalized sense.Comment: 16 pages, 7 figure
No triangles on the moduli space of maximally supersymmetric gauge theory
Maximally supersymmetric gauge theory in four dimensions has a remarkably
simple S-matrix at the origin of its moduli space at both tree and loop level.
This leads to the question what, if any, of this structure survives at the
complement of this one point. Here this question is studied in detail at one
loop for the branch of the moduli space parameterized by a vacuum expectation
value for one complex scalar. Motivated by the parallel D-brane picture of
spontaneous symmetry breaking a simple relation is demonstrated between the
Lagrangian of broken super Yang-Mills theory and that of its higher dimensional
unbroken cousin. Using this relation it is proven both through an on- as well
as an off-shell method there are no so-called triangle coefficients in the
natural basis of one-loop functions at any finite point of the moduli space for
the theory under study. The off-shell method yields in addition absence of
rational terms in a class of theories on the Coulomb branch which includes the
special case of maximal supersymmetry. The results in this article provide
direct field theory evidence for a recently proposed exact dual conformal
symmetry motivated by the AdS/CFT correspondence.Comment: 39 pages, 4 figure
The Beta Ansatz: A Tale of Two Complex Structures
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges
On stability of discretizations of the Helmholtz equation (extended version)
We review the stability properties of several discretizations of the
Helmholtz equation at large wavenumbers. For a model problem in a polygon, a
complete -explicit stability (including -explicit stability of the
continuous problem) and convergence theory for high order finite element
methods is developed. In particular, quasi-optimality is shown for a fixed
number of degrees of freedom per wavelength if the mesh size and the
approximation order are selected such that is sufficiently small and
, and, additionally, appropriate mesh refinement is used near
the vertices. We also review the stability properties of two classes of
numerical schemes that use piecewise solutions of the homogeneous Helmholtz
equation, namely, Least Squares methods and Discontinuous Galerkin (DG)
methods. The latter includes the Ultra Weak Variational Formulation
Note on New KLT relations
In this short note, we present two results about KLT relations discussed in
recent several papers. Our first result is the re-derivation of Mason-Skinner
MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations
directly to MHV amplitude. Our second result is the equivalence proof of the
newly discovered S_{n-2} permutation symmetric KLT relations and the well-known
S_{n-3} permutation symmetric KLT relations. Although both formulas have been
shown to be correct by BCFW recursion relations, our result is the first direct
check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction
Mathematical Modelling of Optical Coherence Tomography
In this chapter a general mathematical model of Optical Coherence Tomography
(OCT) is presented on the basis of the electromagnetic theory. OCT produces
high resolution images of the inner structure of biological tissues. Images are
obtained by measuring the time delay and the intensity of the backscattered
light from the sample considering also the coherence properties of light. The
scattering problem is considered for a weakly scattering medium located far
enough from the detector. The inverse problem is to reconstruct the
susceptibility of the medium given the measurements for different positions of
the mirror. Different approaches are addressed depending on the different
assumptions made about the optical properties of the sample. This procedure is
applied to a full field OCT system and an extension to standard (time and
frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte
Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms
This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a
discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators
A manifestly MHV Lagrangian for N=4 Yang-Mills
We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills
theory in light-cone superspace. This is achieved by constructing a canonical
redefinition which maps the N=4 superfield and its conjugate to a new pair of
superfields. In terms of these new superfields the N=4 Lagrangian takes a
(non-polynomial) manifestly MHV form, containing vertices involving two
superfields of negative helicity and an arbitrary number of superfields of
positive helicity. We also discuss constraints satisfied by the new
superfields, which ensure that they describe the correct degrees of freedom in
the N=4 supermultiplet. We test our derivation by showing that an expansion of
our superspace Lagrangian in component fields reproduces the correct gluon MHV
vertices.Comment: 37 pages, 1 figure. v2: minor changes, references adde
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