42 research outputs found
Pomerons and BCFW recursion relations for strings on D-branes
We derive pomeron vertex operators for bosonic strings and superstrings in
the presence of D-branes. We demonstrate how they can be used in order to
compute the Regge behavior of string amplitudes on D-branes and the amplitude
of ultrarelativistic D-brane scattering. After a lightning review of the BCFW
method, we proceed in a classification of the various BCFW shifts possible in a
field/string theory in the presence of defects/D-branes. The BCFW shifts
present several novel features, such as the possibility of performing single
particle momentum shifts, due to the breaking of momentum conservation in the
directions normal to the defect. Using the pomeron vertices we show that
superstring amplitudes on the disc involving both open and closed strings
should obey BCFW recursion relations. As a particular example, we analyze
explicitly the case of 1 -> 1 scattering of level one closed string states off
a D-brane. Finally, we investigate whether the eikonal Regge regime conjecture
holds in the presence of D-branes.Comment: 49 pages; v2 corrected references and minor typos; v3 minor typos
corrected, version to appear in NP
Interacting Higher Spins and the High Energy Limit of the Bosonic String
In this note, we construct a BRST invariant cubic vertex for massless fields
of arbitrary mixed symmetry in flat space-time. The construction is based on
the vertex given in bosonic Open String Field Theory. The algebra of gauge
transformations is closed without any additional, higher than cubic, couplings
due to the presence of an infinite tower of massless fields. We briefly discuss
the generalization of this result to a curved space-time and other possible
implications.Comment: Published Version; typos corrected, references added; (v3) Some typos
corrected and a minor clarification about eq. (3.29
Primary Fields in Celestial CFT
The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2, â„‚) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere
Primary Fields in Celestial CFT
The basic ingredient of CCFT holography is to regard four-dimensional
amplitudes describing conformal wave packets as two-dimensional conformal
correlation functions of the operators associated to external particles. By
construction, these operators transform as quasi-primary fields under SL(2,C)
conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT
energy-momentum tensor with the operators representing gauge bosons and show
that they transform as Virasoro primaries under diffeomorphisms of the
celestial sphere.Comment: 9 pages. v2: replaced to match JHE
Soft Limits of Yang-Mills Amplitudes and Conformal Correlators
We study tree-level celestial amplitudes in Yang-Mills theory -- Mellin
transforms of multi-gluon scattering amplitudes that convert them into the
correlators of conformal primary fields on two-dimensional celestial sphere. By
using purely field-theoretical methods, we show that the soft conformal limit
of celestial amplitudes, in which one of the primary field operators associated
to gauge bosons becomes a dimension one current, is dominated by the
contributions of low-energy soft particles. This result confirms conclusions
reached by using Yang-Mills theory formulated in curvilinear coordinates, as
pioneered by Strominger. By using well-known collinear limits of Yang-Mills
amplitudes, we derive the OPE rules for the primary fields and the holomorphic
currents arising in the conformally soft limit. The Ward identities following
from OPE have the same form as the identities derived by using soft theorems.Comment: 16 pages. v2: 1 reference adde
Soft Limits of Yang-Mills Amplitudes and Conformal Correlators
We study tree-level celestial amplitudes in Yang-Mills theory — Mellin transforms of multi-gluon scattering amplitudes that convert them into the correlators of conformal primary fields on two-dimensional celestial sphere. By using purely field-theoretical methods, we show that the soft conformal limit of celestial amplitudes, in which one of the primary field operators associated to gauge bosons becomes a dimension one current, is dominated by the contributions of low-energy soft particles. This result confirms conclusions reached by using Yang-Mills theory formulated in curvilinear coordinates, as pioneered by Strominger. By using well-known collinear limits of Yang-Mills amplitudes, we derive the OPE rules for the primary fields and the holomorphic currents arising in the conformally soft limit. The Ward identities following from OPE have the same form as the identities derived by using soft theorems
Extended Super BMS Algebra of Celestial CFT
We study two-dimensional celestial conformal field theory describing
four-dimensional supergravity/Yang-Mills systems and show that the
underlying symmetry is a supersymmetric generalization of BMS symmetry. We
construct fermionic conformal primary wave functions and show how they are
related via supersymmetry to their bosonic partners. We use soft and collinear
theorems of supersymmetric Einstein-Yang-Mills theory to derive the OPEs of the
operators associated to massless particles. The bosonic and fermionic soft
theorems are shown to form a sequence under supersymmetric Ward identities. In
analogy with the energy momentum tensor, the supercurrents are shadow
transforms of soft gravitino operators and generate an infinite-dimensional
supersymmetry algebra. The algebra of generators agrees
with the expectations based on earlier work on the asymptotic symmetry group of
supergravity. We also show that the supertranslation operator can be written as
a product of holomorphic and anti-holomorphic supercurrents.Comment: 44 pages. v2: subsec. 7.4 added, typos fixe
Conformal Blocks from Celestial Gluon Amplitudes
In celestial conformal field theory, gluons are represented by primary fields
with dimensions , and spin ,
in the adjoint representation of the gauge group. All two- and three-point
correlation functions of these fields are zero as a consequence of
four-dimensional kinematic constraints. Four-point correlation functions
contain delta-function singularities enforcing planarity of four-particle
scattering events. We relax these constraints by taking a shadow transform of
one field and perform conformal block decomposition of the corresponding
correlators. We compute the conformal block coefficients. When decomposed in
channels that are "compatible" in two and four dimensions, such four-point
correlators contain conformal blocks of primary fields with dimensions
, where is an integer, with integer spin
. They appear in all gauge group representations
obtained from a tensor product of two adjoint representations. When decomposed
in incompatible channels, they also contain primary fields with continuous
complex spin, but with positive integer dimensions.Comment: 16 pages. v2: coefficients simplifie
Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
We propose a method of construction of a cubic interaction in massless Higher
Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions.
We consider a triplet formulation of the Higher Spin gauge theory and
generalize the Higher Spin symmetry algebra of the free model to the
corresponding algebra for the case of cubic interaction. The generators of this
new algebra carry indexes which label the three Higher Spin fields involved
into the cubic interaction. The method is based on the use of oscillator
formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive
general conditions on the form of cubic interaction vertex and discuss the
ambiguities of the vertex which result from field redefinitions. This method
can in principle be applied for constructing the Higher Spin interaction vertex
at any order. Our results are a first step towards the construction of a
Lagrangian for interacting Higher Spin gauge fields that can be holographically
studied.Comment: Published Version; comments added in introduction; minor typos and
references correcte