169 research outputs found
Three particle superstring amplitudes with massive legs
On-shell superspaces and associated spinor helicity techniques give an
efficient formulation of the Ward identities of on-shell supersymmetry for
scattering amplitudes and supply tools to construct their solutions. Based on
these techniques in this paper the general solutions of the Ward identities are
presented for three particle scattering amplitudes with one, two or three
massive legs for simple supersymmetry in ten and eight dimensions. It is shown
in examples how these solutions may be used to obtain concrete amplitudes for
the closed (IIB) and open superstring in a flat background. Explicit results
include all three point amplitudes with one massive leg whose functional form
is shown to be dictated completely by super-Poincare symmetry. The resulting
surprisingly simple series only involves massive superfields labelled by
completely symmetric little group representations. The extension to more
general explicit three and higher point amplitudes in string theory is
initiated. In appendices the field content of the fundamental massive
superfields of the open and closed superstring are listed in terms of the
Dynkin labels of a variety of groups which may be of independent interest.Comment: 45 pages. v2: typos corrected, references adde
The Whitham Deformation of the Dijkgraaf-Vafa Theory
We discuss the Whitham deformation of the effective superpotential in the
Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of
an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we
derive the Whitham equation for the period, which governs flowings of branch
points on the Riemann surface. By studying the hodograph solution to the
Whitham equation it is shown that the effective superpotential in the DV theory
is realized by many different meromorphic differentials. Depending on which
meromorphic differential to take, the effective superpotential undergoes
different deformations. This aspect of the DV theory is discussed in detail by
taking the N=1^* theory. We give a physical interpretation of the deformation
parameters.Comment: 35pages, 1 figure; v2: one section added to give a physical
interpretation of the deformation parameters, one reference added, minor
corrections; v4: minor correction
On correlation functions of Wilson loops, local and non-local operators
We discuss and extend recent conjectures relating partial null limits of
correlation functions of local gauge invariant operators and the expectation
value of null polygonal Wilson loops and local gauge invariant operators. We
point out that a particular partial null limit provides a strategy for the
calculation of the anomalous dimension of short twist-two operators at weak and
strong coupling.Comment: 29 pages, 8 figure
On-shell Recursion in String Theory
We prove that all open string theory disc amplitudes in a flat background
obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a
possible reality condition on a kinematic invariant. Arguments that the same
holds for tree level closed string amplitudes are given as well. Non-adjacent
BCFW-shifts are related to adjacent shifts through monodromy relations for
which we provide a novel CFT based derivation. All possible recursion relations
are related by old-fashioned string duality. The field theory limit of the
analysis for amplitudes involving gluons is explicitly shown to be smooth for
both the bosonic string as well as the superstring. In addition to a proof a
less rigorous but more powerful argument based on the underlying CFT is
presented which suggests that the technique may extend to a much more general
setting in string theory. This is illustrated by a discussion of the open
string in a constant B-field background and the closed string on the level of
the sphere.Comment: 36 + 9 pages text, one figure, v3: added discussion on relation to
old-fashioned factorization, typos corrected, published versio
Adding flavour to twistor strings
Twistor string theory is known to describe a wide variety of field theories
at tree-level and has proved extremely useful in making substantial progress in
perturbative gauge theory. We explore the twistor dual description of a class
of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding
'flavour' branes to the topological B-model on super-twistor space and comment
on the appearance of these objects. Evidence for the correspondence is provided
by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical
Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3:
Typos correcte
On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
We study the relationship between the momentum twistor MHV vertex expansion
of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of
the BCFW recursion relations. We demonstrate explicitly in several examples
that the MHV vertex expressions for tree-level amplitudes and loop integrands
satisfy the recursion relations. Furthermore, we introduce a rewriting of the
MHV expansion in terms of sums over non-crossing partitions and show that this
cyclically invariant formula satisfies the recursion relations for all numbers
of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and
discussion, updated references, typos fixe
Nonperturbative Superpotentials and Compactification to Three Dimensions
We consider four-dimensional N=2 supersymmetric gauge theories with gauge
group U(N) on R^3 x S^1, in the presence of a classical superpotential. The
low-energy quantum superpotential is obtained by simply replacing the adjoint
scalar superfield in the classical superpotential by the Lax matrix of the
integrable system that underlies the 4d field theory. We verify in a number of
examples that the vacuum structure obtained in this way matches precisely that
in 4d, although the degrees of freedom that appear are quite distinct. Several
features of 4d field theories, such as the possibility of lifting vacua from
U(N) to U(tN), become particularly simple in this framework. It turns out that
supersymmetric vacua give rise to a reduction of the integrable system which
contains information about the field theory but also about the Dijkgraaf-Vafa
matrix model. The relation between the matrix model and the quantum
superpotential on R^3 x S^1 appears to involve a novel kind of mirror symmetry.Comment: LaTeX, 45 pages, uses AmsMath, minor correction, reference adde
Massive amplitudes on the Coulomb branch of N=4 SYM
We initiate a systematic study of amplitudes with massive external particles
on the Coulomb-branch of N=4 super Yang Mills theory: 1) We propose that
(multi-)soft-scalar limits of massless amplitudes at the origin of moduli space
can be used to determine Coulomb-branch amplitudes to leading order in the
mass. This is demonstrated in numerous examples. 2) We find compact explicit
expressions for several towers of tree-level amplitudes, including scattering
of two massive W-bosons with any number of positive helicity gluons, valid for
all values of the mass. 3) We present the general structure of superamplitudes
on the Coulomb branch. For example, the n-point "MHV-band" superamplitude is
proportional to a Grassmann polynomial of mixed degree 4 to 12, which is
uniquely determined by supersymmetry. We find explicit tree-level
superamplitudes for this MHV band and for other simple sectors of the theory.
4) Dual conformal generators are constructed, and we explore the dual conformal
properties of the simplest massive amplitudes. Our compact expressions for
amplitudes and superamplitudes should be of both theoretical and
phenomenological interest; in particular the tree-level results carry over to
truncations of the theory with less supersymmetry.Comment: 29 pages, 1 figur
- …