21 research outputs found
One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so
called scattering amplitudes at one-loop, in order to obtain quadratic
propagators. In theories with colour ordering the key ingredient is the
redefinition of the Parke-Taylor factors. After classifying all the possible
one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless
Bi-adjoint theory. The prescription directly reproduces the quadratic
propagators from of the traditional Feynman approach.Comment: 43 pages, new appendix added, few typos corrected. Accepted for
publication in JHE
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
We consider the nonrelativistic limit of the abelian reduction of the massive
ABJM model proposed in \cite{Mohammed:2012gi}, obtaining a supersymmetric
version of the Jackiw-Pi model. The system exhibits an
Super-Schr\"odinger symmetry with the Jackiw-Pi vortices emerging as BPS
solutions. We find that this -dimensional abelian field theory is dual
to a certain (3+1)-dimensional gravity theory that differs somewhat from
previously considered abelian condensed matter stand-ins for the ABJM model. We
close by commenting on progress in the top-down realization of the AdS/CMT
correspondence in a critical string theory.Comment: 24 pages, no figures; clarifying remarks added, references added,
typos correcte
Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
In this work we have studied the Kleiss-Kuijf relations for the recently
introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce
quadratic Feynman propagators. By doing this, we were able to identify the
non-planar one-loop Parke-Taylor factors. In order to check that, in fact,
these new factors can describe non-planar amplitudes, we applied them to the
bi-adjoint theory. As a byproduct, we found a new type of graphs that
we called the non-planar CHY-graphs. These graphs encode all the information
for the subleading order at one-loop, and there is not an equivalent of these
in the Feynman formalism.Comment: 35 pages, typos corrected, references adde
Conductivity in the gravity dual to massive ABJM and the membrane paradigm
In this paper we analyze the effect of the massive deformation of the ABJM
model on the calculation of conductivity of the dual theory. We show that some
of the difficulties presented by the dual geometry, in particular the
construction of black holes therein, can be at least partially circumvented by
adopting a membrane paradigm-like computation of the conductivity, which
requires us to know just the effect of the deformation on the {\it horizon} of
a black hole in AdS. The deformation at the horizon itself is found by
first deforming the flat space near the horizon, and then using the
corresponding solution near the horizon as initial conditions for the
Einstein's equations. We find the same result, showing an increase in
conductivity, using two types of membrane paradigm computations.Comment: 28 pages, explanations added, paragraph added at the end of section
The QED four -- photon amplitudes off-shell: part 1
The QED four-photon amplitude has been well-studied by many authors, and
on-shell is treated in many textbooks. However, a calculation with all four
photons off-shell is presently still lacking, despite of the fact that this
amplitude appears off-shell as a subprocess in many different contexts, in
vacuum as well as with some photons connecting to external fields. The present
paper is the first in a series of four where we use the worldline formalism to
obtain this amplitude explicitly in terms of hypergeometric functions, and
derivatives thereof, for both scalar and spinor QED. The formalism allows us to
unify the scalar and spinor loop calculations, to avoid the usual breaking up
of the amplitude into three inequivalent Feynman diagrams, and to achieve
manifest transversality as well as UV finiteness at the integrand level by an
optimized version of the integration-by-parts procedure originally introduced
by Bern and Kosower for gluon amplitudes. The full permutation symmetry is
maintained throughout, and the amplitudes get projected naturally into the
basis of five tensors introduced by Costantini et al. in 1971. Since in many
applications of the "four-photon box" some of the photons can be taken in the
low-energy limit, and the formalism makes it easy to integrate out any such
leg, apart from the case of general kinematics (part 4) we also treat the
special cases of one (part 3) or two (part 2) photons taken at low energy. In
this first part of the series, we summarize the application of the worldline
formalism to the N-photon amplitudes and its relation to Feynman diagrams,
derive the optimized tensor-decomposed integrands of the four-photon amplitudes
in scalar and spinor QED, and outline the computational strategy to be followed
in parts 2 to 4.Comment: 38 pages, 14 figure
One-loop off-shell amplitudes from classical equations of motion
In this letter we present a recursive method for computing one-loop off-shell
amplitudes in colored quantum field theories. First, we generalize the
perturbiner method by recasting the multiparticle currents as generators of
off-shell tree level amplitudes. After, by taking advantage of the underlying
color structure, we define a consistent sewing procedure to iteratively compute
the one-loop integrands. When gauge symmetries are involved, the whole
procedure is extended to multiparticle solutions involving ghosts, which can
then be accounted for in the full loop computation. Since the required input
here is equations of motion and gauge symmetry, our framework naturally extends
to one-loop computations in certain non-Lagrangian field theories.Comment: 7 pages. v2: clarifications and references added. Matches published
version. v3: cyclic completion rule of equation (1.4) restored as in v1,
supersedes the published versio
The structure of gauge theories with matter
In this work we present an algebraic approach to the dynamics and
perturbation theory at tree-level for gauge theories coupled to matter. The
field theories we will consider are: Chern-Simons-Matter, Quantum
Chromodynamics, and scalar Quantum Chromodynamics. Starting with the
construction of the master action in the classical Batalin-Vilkovisky
formalism, we will extract the -algebra that allow us to
recursively calculate the perturbiner expansion from its minimal model. The
Maurer-Cartan action obtained in this procedure will then motivate a generating
function for all the tree-level scattering amplitudes. There are two
interesting outcomes of this construction: a generator for fully-flavoured
amplitudes via a localisation on Dyck words; and closed expressions for fermion
and scalar lines attached to -gluons with arbitrary polarisations.Comment: 59 pages, final versio
One-Loop Yang-Mills Integrands from Scattering Equations
We investigate in the context of the scattering equations, how one-loop
linear propagator integrands in gauge theories can be linked to integrands with
quadratic propagators using a double forward limit. We illustrate our procedure
through examples and demonstrate how the different parts of the derived
quadratic integrand are consistent with cut-integrands derived from
four-dimensional generalized unitarity. We also comment on applications and
discuss possible further generalizations.Comment: 20 pages, 6 figures, typos corrected, added clarifications and
comments. Version to be published in PR
Eliminating ambiguities for quantum corrections to strings moving in
We apply a physical principle, previously used to eliminate ambiguities in
quantum corrections to the 2 dimensional kink, to the case of spinning strings
moving in , thought of as another kind of two
dimensional soliton. We find that this eliminates the ambiguities and selects
the result compatible with AdS/CFT, providing a solid foundation for one of the
previous calculations, which found agreement. The method can be applied to
other classical string "solitons".Comment: 18 pages, latex; references added, comments added at end of section
4, a few words changed; footnote added on page 1