74,619 research outputs found
Scattering Amplitudes For All Masses and Spins
We introduce a formalism for describing four-dimensional scattering
amplitudes for particles of any mass and spin. This naturally extends the
familiar spinor-helicity formalism for massless particles to one where these
variables carry an extra SU(2) little group index for massive particles, with
the amplitudes for spin S particles transforming as symmetric rank 2S tensors.
We systematically characterise all possible three particle amplitudes
compatible with Poincare symmetry. Unitarity, in the form of consistent
factorization, imposes algebraic conditions that can be used to construct all
possible four-particle tree amplitudes. This also gives us a convenient basis
in which to expand all possible four-particle amplitudes in terms of what can
be called "spinning polynomials". Many general results of quantum field theory
follow the analysis of four-particle scattering, ranging from the set of all
possible consistent theories for massless particles, to spin-statistics, and
the Weinberg-Witten theorem. We also find a transparent understanding for why
massive particles of sufficiently high spin can not be "elementary". The Higgs
and Super-Higgs mechanisms are naturally discovered as an infrared unification
of many disparate helicity amplitudes into a smaller number of massive
amplitudes, with a simple understanding for why this can't be extended to
Higgsing for gravitons. We illustrate a number of applications of the formalism
at one-loop, giving few-line computations of the electron (g-2) as well as the
beta function and rational terms in QCD. "Off-shell" observables like
correlation functions and form-factors can be thought of as scattering
amplitudes with external "probe" particles of general mass and spin, so all
these objects--amplitudes, form factors and correlators, can be studied from a
common on-shell perspective.Comment: 79 page
Detection of Symmetry Enriched Topological Phases
Topologically ordered systems in the presence of symmetries can exhibit new
structures which are referred to as symmetry enriched topological (SET) phases.
We introduce simple methods to detect the SET order directly from a complete
set of topologically degenerate ground state wave functions. In particular, we
first show how to directly determine the characteristic symmetry
fractionalization of the quasiparticles from the reduced density matrix of the
minimally entangled states. Second, we show how a simple generalization of a
non-local order parameter can be measured to detect SETs. The usefulness of the
proposed approached is demonstrated by examining two concrete model states
which exhibit SET: (i) a spin-1 model on the honeycomb lattice and (ii) the
resonating valence bond state on a kagome lattice. We conclude that the spin-1
model and the RVB state are in the same SET phases
Exact coefficients for higher dimensional operators with sixteen supersymmetries
We consider constraints on higher dimensional operators for supersymmetric
effective field theories. In four dimensions with maximal supersymmetry and
SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F^n
with MHV helicity configurations must satisfy a recursion relation, and are
completely determined by that of F^4. As the F^4 coefficient is known to be
one-loop exact, this allows us to derive exact coefficients for all such
operators. We also argue that the results are consistent with the SL(2,Z)
duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb
branch effective action, we again find an infinite class of operators whose
coefficient that are determined exactly. We also consider three-dimensional N=8
as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we
demonstrate that the coefficient of dimension-six operator must be proportional
to the square of that of dimension-four.Comment: typos corrected, minor modificatio
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