152 research outputs found
Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
The IR divergences of supergravity amplitudes are less severe than those of
planar SYM amplitudes, and are comparable to those subleading-color SYM
amplitudes that are most subleading in the 1/N expansion, namely O(1/epsilon^L)
for L-loop amplitudes. We derive linear relations between one- and two-loop
four-point amplitudes and one-loop five-point amplitudes of N = 4, 5, and 6
supergravity and the most-subleading-color contributions of the analogous
amplitudes of N = 0, 1, and 2 SYM theory, extending earlier results for N = 8
supergravity amplitudes. Our work relies on linear relations between N >= 4
supergravity and planar SYM amplitudes that were recently derived using the
double-copy property of gravity, and color-kinematic duality of gauge theories.Comment: 21 pages, 1 figur
Penner Type Matrix Model and Seiberg-Witten Theory
We discuss the Penner type matrix model recently proposed by Dijkgraaf and
Vafa for a possible explanation of the relation between four-dimensional gauge
theory and Liouville theory by making use of the connection of the matrix model
to two-dimensional CFT. We first consider the relation of gauge couplings
defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory
being related as . We then use this relation to discuss the action of modular
transformation on the matrix model and determine its spectral curve.
We also discuss the decoupling of massive flavors from the N_f = 4 matrix
model and derive matrix models describing asymptotically free N = 2 gauge
theories. We find that the Penner type matrix theory reproduces correctly the
standard results of N = 2 supersymmetric gauge theories.Comment: 22 pages; v2: references added, typos corrected; v3: a version to
appear in JHE
Eikonal methods applied to gravitational scattering amplitudes
We apply factorization and eikonal methods from gauge theories to scattering
amplitudes in gravity. We hypothesize that these amplitudes factor into an
IR-divergent soft function and an IR-finite hard function, with the former
given by the expectation value of a product of gravitational Wilson line
operators. Using this approach, we show that the IR-divergent part of the
n-graviton scattering amplitude is given by the exponential of the one-loop IR
divergence, as originally discovered by Weinberg, with no additional subleading
IR-divergent contributions in dimensional regularization.Comment: 16 pages, 3 figures; v2: title change and minor rewording (published
version); v3: typos corrected in eqs.(3.2),(4.1
One-loop SYM-supergravity relation for five-point amplitudes
We derive a linear relation between the one-loop five-point amplitude of N=8
supergravity and the one-loop five-point subleading-color amplitudes of N=4
supersymmetric Yang-Mills theory.Comment: 17 pages, 2 figures; v2: very minor correction
CHY representations for gauge theory and gravity amplitudes with up to three massive particles
We show that a wide class of tree-level scattering amplitudes involving
scalars, gauge bosons, and gravitons, up to three of which may be massive, can
be expressed in terms of a Cachazo-He-Yuan representation as a sum over
solutions of the scattering equations. These amplitudes, when expressed in
terms of the appropriate kinematic invariants, are independent of the masses
and therefore identical to the corresponding massless amplitudes.Comment: 20 pages, 1 figure; v2: minor typos corrected, published versio
On the renormalization of multiparton webs
We consider the recently developed diagrammatic approach to soft-gluon
exponentiation in multiparton scattering amplitudes, where the exponent is
written as a sum of webs - closed sets of diagrams whose colour and kinematic
parts are entangled via mixing matrices. A complementary approach to
exponentiation is based on the multiplicative renormalizability of intersecting
Wilson lines, and their subsequent finite anomalous dimension. Relating this
framework to that of webs, we derive renormalization constraints expressing all
multiple poles of any given web in terms of lower-order webs. We examine these
constraints explicitly up to four loops, and find that they are realised
through the action of the web mixing matrices in conjunction with the fact that
multiple pole terms in each diagram reduce to sums of products of lower-loop
integrals. Relevant singularities of multi-eikonal amplitudes up to three loops
are calculated in dimensional regularization using an exponential infrared
regulator. Finally, we formulate a new conjecture for web mixing matrices,
involving a weighted sum over column entries. Our results form an important
step in understanding non-Abelian exponentiation in multiparton amplitudes, and
pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure
The Complete KLT-Map Between Gravity and Gauge Theories
We present the complete map of any pair of super Yang-Mills theories to
supergravity theories as dictated by the KLT relations in four dimensions.
Symmetries and the full set of associated vanishing identities are derived. A
graphical method is introduced which simplifies counting of states, and helps
in identifying the relevant set of symmetries.Comment: 41 pages, 16 figures, published version, typos corrected, references
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