12,201 research outputs found
Seiberg Duality in Matrix Model
In this paper, we use the matrix model of pure fundamental flavors (without
the adjoint field) to check the Seiberg duality in the case of complete mass
deformation. We show that, by explicit integration at both sides of electric
and magnetic matrix models, the results agree with the prediction in the field
theory.Comment: 5 pages. Short notes. Abstract rewritten. Typo fixe
Note on differential operators, CHY integrands, and unifying relations for amplitudes
An elegant unified web for amplitudes of various theories was given by
Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar
web has also been constructed by Cheung, Shen and Wen, which relies on a set of
differential operators. In this note, by acting these differential operators on
CHY-integrands systematically, we have established the relation between these
two approaches. Thus, amplitudes for all theories which have CHY
representations, include gravity theory, Einstein-Yang-Mills theory,
Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory,
Born-Infeld theory, Dirac-Born-Infeld theory and its extension, bi-adjoint
scalar theory, theory, non-linear sigma model, as well as special
Galileon theory, have been included in the unified web rooted from gravity
theory.Comment: 20 page
Cross Section Evaluation by Spinor Integration II: The massive case in 4D
In this paper, we continue our study of calculating the cross section by the
spinor method, i.e., performing the phase space integration using the spinor
method. We have focused on the case where the physical momenta are massive and
in pure 4D. We established the framework of such a new method and presented
several examples, including two real progresses: and
.Comment: 23 pages, 1 figure;further comments and references adde
The classification of two-loop integrand basis in pure four-dimension
In this paper, we have made the attempt to classify the integrand basis of
all two-loop diagrams in pure four-dimension space-time. Our classification
includes the topology of two-loop diagrams which determines the structure of
denominators, and the set of numerators under different kinematic
configurations of external momenta by using Gr\"{o}bner basis method. In our
study, the variety defined by setting all propagators to on-shell has played an
important role. We discuss the structure of variety and how it splits to
various irreducible branches when external momenta at each corner of diagrams
satisfy some special kinematic conditions. This information is crucial to the
numerical or analytical fitting of coefficients for integrand basis in
reduction process.Comment: 52 pages, 9 figures. v2 reference added, v3 published versio
Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of
tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary
number of gluons and gravitons, which is valid for general spacetime dimensions
and any helicity configurations. The recursion is written in terms of
fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be
further carried out until we reach an expansion in terms of pure YM amplitudes
in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning
tree structure rooted on gluons whose vertices are gravitons. We further
propose a set of graph theoretical rules based on spanning trees that evaluate
directly the pure YM expansion coefficients.Comment: 36 pages, 3 captioned figures; v2: more details added, revised and
published versio
Note on Identities Inspired by New Soft Theorems
The new soft theorems, for both gravity and gauge amplitudes, have inspired a
number of works, including the discovery of new identities related to
amplitudes. In this note, we present the proof and discussion for two sets of
identities. The first set includes an identity involving the half-soft function
which had been used in the soft theorem for one-loop rational gravity
amplitudes, and another simpler identity as its byproduct. The second set
includes two identities involving the KLT momentum kernel, as the consistency
conditions of the KLT relation plus soft theorems for both gravity and gauge
amplitudes. We use the CHY formulation to prove the first identity, and
transform the second one into a convenient form for future discussion.Comment: 17 page
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