217 research outputs found
On-shell supersymmetry for massive multiplets
The consequences of on-shell supersymmetry are studied for scattering
amplitudes with massive particles in four dimensions. Using the massive version
of the spinor helicity formalism the supersymmetry transformations relating
products of on-shell states are derived directly from the on-shell
supersymmetry algebra for any massive representation. Solutions to the
resulting Ward identities can be constructed as functions on the on-shell
superspaces that are obtained from the coherent state method. In simple cases
it is shown that these superspaces allow one to construct explicitly
supersymmetric scattering amplitudes. Supersymmetric on-shell recursion
relations for tree-level superamplitudes with massive particles are introduced.
As examples, simple supersymmetric amplitudes are constructed in SQCD, the
Abelian Higgs model, the Coulomb branch of N=4 super Yang-Mills, QCD with an
effective Higgs-gluon coupling and for massive vector boson currents.Comment: 49+9 pages, 4 figures, v2: references updated, typos corrected,
examples added, v3: final PRD versio
Symmetries of the Self-Dual Sector of N=4 Super Yang-Mills on the Light Cone
A recent paper proposes a way of constructing infinite dimensional symmetries
of the non-supersymmetric self-dual Yang-Mills action using isometries of the
space-time. We review the Lagrangian formulation of N = 4 super Yang-Mills MHV
rules and extend the approach taken for the non-supersymmetric case to
construct infinite dimensional symmetries of self-dual N = 4 super Yang-Mills.Comment: 22 pages, 8 figures. V[2] Added references and minor typographical
correction
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
Simple superamplitudes in higher dimensions
We provide simple superspaces based on a formulation of spinor helicity in
general even dimensions. As a distinguishing feature these spaces admit a
fermionic super-momentum conserving delta function solution to the on-shell
supersymmetry Ward identities. Using these solutions, we present beautifully
simple formulae for the complete three, four and five point superamplitudes in
maximal super Yang-Mills theory in eight dimensions, and for the three and four
point superamplitudes in ten dimensional type IIB supergravity. In addition, we
discuss the exceptional kinematics of the three point amplitude, and the
supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page
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
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
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
Tree-Level Formalism
We review two novel techniques used to calculate tree-level scattering
amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the
MHV diagrams, we consider applications to tree-level amplitudes and focus in
particular on the N=4 supersymmetric formulation. We also briefly describe the
derivation of loop amplitudes using MHV diagrams. For the recursion relations,
after presenting their general proof, we discuss several applications to
massless theories with and without supersymmetry, to theories with massive
particles, and to graviton amplitudes in General Relativity. This article is an
invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of
Physics A devoted to "Scattering Amplitudes in Gauge Theories", R.
Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections,
references adde
N=1 G_2 SYM theory and Compactification to Three Dimensions
We study four dimensional N=2 G_2 supersymmetric gauge theory on R^3\times
S^1 deformed by a tree level superpotential. We will show that the exact
superpotential can be obtained by making use of the Lax matrix of the
corresponding integrable model which is the periodic Toda lattice based on the
dual of the affine G_2 Lie algebra. At extrema of the superpotential the
Seiberg-Witten curve typically factorizes, and we study the algebraic equations
underlying this factorization. For U(N) theories the factorization was closely
related to the geometrical engineering of such gauge theories and to matrix
model descriptions, but here we will find that the geometrical interpretation
is more mysterious. Along the way we give a method to compute the gauge theory
resolvent and a suitable set of one-forms on the Seiberg-Witten curve. We will
also find evidence that the low-energy dynamics of G_2 gauge theories can
effectively be described in terms of an auxiliary hyperelliptic curve.Comment: 27 pages, late
- …