127 research outputs found
Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary Conditions
It is well known that integrable charges for short-range (e.g.
nearest-neighbor) spin chains with periodic boundary conditions can be
recursively generated by a so-called boost operator. In the past, this
iterative construction has been generalized to periodic long-range spin chains
as they appear in the context of the gauge/gravity correspondence. Here we
introduce recursion relations for open long-range spin chain charges converting
a short-range into a long-range integrable model.Comment: 5 pages, 2 figures, v2: comments adde
Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in
N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman
diagram calculations, solutions to these constraints, namely the four- and
six-point superamplitudes, are presented and shown to be invariant under
Yangian symmetry. This introduces integrability into the amplitude sector of
the theory.Comment: 50 pages. v2, v3: References added, minor correction
Hidden Conformal Symmetry in Tree-Level Graviton Scattering
We argue that the scattering of gravitons in ordinary Einstein gravity
possesses a hidden conformal symmetry at tree level in any number of
dimensions. The presence of this conformal symmetry is indicated by the dilaton
soft theorem in string theory, and it is reminiscent of the conformal
invariance of gluon tree-level amplitudes in four dimensions. To motivate the
underlying prescription, we demonstrate that formulating the conformal symmetry
of gluon amplitudes in terms of momenta and polarization vectors requires
manifest reversal and cyclic symmetry. Similarly, our formulation of the
conformal symmetry of graviton amplitudes relies on a manifestly permutation
symmetric form of the amplitude function.Comment: 35 pages, 3 figure
Consistent Conformal Extensions of the Standard Model
The question of whether classically conformal modifications of the standard
model are consistent with experimental obervations has recently been subject to
renewed interest. The method of Gildener and Weinberg provides a natural
framework for the study of the effective potential of the resulting
multi-scalar standard model extensions. This approach relies on the assumption
of the ordinary loop hierarchy of scalar
and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently
argued that in the (single-scalar) standard model, gauge invariant results
require the consistent scaling . In the
present paper we contrast these two hierarchy assumptions and illustrate the
differences in the phenomenological predictions of minimal conformal extensions
of the standard model.Comment: 20 pages, 19 figures. v2: Typo in (3.3) corrected, references adde
The Weinberg-Witten theorem on massless particles: an essay
In this essay we deal with the Weinberg-Witten theorem [1] which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincaré group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincaré covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories
Massive Conformal Symmetry and Integrability for Feynman Integrals
In the context of planar holography, integrability plays an important role
for solving certain massless quantum field theories such as N=4 SYM theory. In
this letter we show that integrability also features in the building blocks of
massive quantum field theories. At one-loop order we prove that all massive
n-gon Feynman integrals in generic spacetime dimensions are invariant under a
massive Yangian symmetry. At two loops similar statements can be proven for
graphs built from two n-gons. At generic loop order we conjecture that all
graphs cut from regular tilings of the plane with massive propagators on the
boundary are invariant. We support this conjecture by a number of numerical
tests for higher loops and legs. The observed Yangian extends the bosonic part
of the massive dual conformal symmetry that was found a decade ago on the
Coulomb branch of N=4 SYM theory. By translating the Yangian level-one
generators from dual to original momentum space, we introduce a massive
generalization of momentum space conformal symmetry. Even for non-dual
conformal integrals this novel symmetry persists. The Yangian can thus be
understood as the closure of massive dual conformal symmetry and this new
massive momentum space conformal symmetry, which suggests an interpretation via
AdS/CFT. As an application of our findings, we bootstrap the hypergeometric
building blocks for examples of massive Feynman integrals.Comment: 6 pages, v2: typos corrected, clarifications added, v3: minor
improvements/corrections, title adapted to journal titl
Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
We study Yangian-invariant deformations of scattering amplitudes in 4d N=4
supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena
(ABJM) theory. In particular, we obtain the deformed Grassmannian integral for
4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space.
For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We
investigate general deformations of on-shell diagrams, and find the deformed
Grassmannian integral for this theory. We furthermore introduce the algebraic
R-matrix construction of deformed Yangian invariants for ABJM theory.Comment: 39 pages, 9 figures; v2: references added, typos fixed, section 3.4
improved, published versio
- …