12,910 research outputs found
Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
To explore color/kinematics duality for general representations of the gauge
group we formulate the duality for general abelian orbifolds of the SU(N), N=4
super Yang-Mills theory in four dimensions, which have fields in the
bi-fundamental representation, and use it to construct explicitly complete
four-vector and four-scalar amplitudes at one loop. For fixed number of
supercharges, graph-organized L-loop n-point integrands of all orbifold
theories are given in terms of a fixed set of polynomials labeled by L
representations of the orbifold group. In contrast to the standard
duality-satisfying presentation of amplitudes of the N=4 super Yang-Mills
theory, each graph may appear several times with different internal states. The
color and R-charge flow provide a way to deform the amplitudes of orbifold
theories to those of more general quiver gauge theories which do not
necessarily exhibit color/kinematics duality on their own. Based on the
organization of amplitudes required by the duality between color and kinematics
in orbifold theories we show how the amplitudes of certain non-factorized
matter-coupled supergravity theories can be found through a double-copy
construction. We also carry out a comprehensive search for theories with fields
solely in the adjoint representation of the gauge group and amplitudes
exhibiting color/kinematics duality for all external states and find an
interesting relation between supersymmetry and existence of the duality.Comment: 51 pages, 7 figures, PDFLaTex, typos fixed, minor changes in section
3.
Tilting Cohen-Macaulay representations
This is a survey on recent developments in Cohen-Macaulay representations via
tilting and cluster tilting theory. We explain triangle equivalences between
the singularity categories of Gorenstein rings and the derived (or cluster)
categories of finite dimensional algebras.Comment: To appear in the ICM 2018 proceeding
Generic multiloop methods and application to N=4 super-Yang-Mills
We review some recent additions to the tool-chest of techniques for finding
compact integrand representations of multiloop gauge-theory amplitudes -
including non-planar contributions - applicable for N=4 super-Yang-Mills in
four and higher dimensions, as well as for theories with less supersymmetry. We
discuss a general organization of amplitudes in terms of purely cubic graphs,
review the method of maximal cuts, as well as some special D-dimensional
recursive cuts, and conclude by describing the efficient organization of
amplitudes resulting from the conjectured duality between color and kinematic
structures on constituent graphs.Comment: 42 pages, 18 figures, invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor
corrections, v3 added reference
Basic hypergeometry of supersymmetric dualities
We introduce several new identities combining basic hypergeometric sums and
integrals. Such identities appear in the context of superconformal index
computations for three-dimensional supersymmetric dual theories. We give both
analytic proofs and physical interpretations of the presented identities.Comment: 25 pages, v2: minor corrections and comment
Dual expansions of N=4 super Yang-Mills theory via IIB superstring theory
We examine the dual correspondence between holographic IIB superstring theory
and N=4 super Yang-Mills theory at finite values of the coupling constants. In
particular we analyze a field theory strong-coupling expansion which is the
S-dual of the planar expansion. This expansion arises naturally as the AdS/CFT
dual of the IIB superstring scattering amplitudes given a genus truncation
property due to modular invariance. The space-time structure of the
contributions to the field theory four-point correlation functions obtained
from the IIB scattering elements is investigated in the example of the product
of four conserved stress tensors, and is expressed as an infinite sum of field
theory triangle integrals. The OPE structure of these contributions to the
stress tensor four-point function is analyzed and shown not to give rise to any
poles. Quantization of the string in the background of a five-form field
strength is performed through a covariantized background field approach, and
relations to the N=4 topological string are found.Comment: LaTeX, 40 pages, 5 figure
Double-Copy Constructions and Unitarity Cuts
The duality between color and kinematics enables the construction of
multiloop gravity integrands directly from corresponding gauge-theory
integrands. This has led to new nontrivial insights into the structure of
gravity theories, including the discovery of enhanced ultraviolet
cancellations. To continue to gain deeper understandings and probe these new
properties, it is crucial to further improve techniques for constructing
multiloop gravity integrands. In this paper, we show by example how one can
alleviate difficulties encountered at the multiloop level by relaxing the
color-kinematics duality conditions to hold manifestly only on unitarity cuts
instead of globally on loop integrands. As an example, we use a minimal ansatz
to construct an integrand for the two-loop four-point nonsupersymmetric pure
Yang-Mills amplitude in dimensions that is compatible with these relaxed
color-kinematics duality constraints. We then immediately obtain a
corresponding gravity integrand through the double-copy procedure. Comments on
ultraviolet divergences are also included.Comment: 26 pages, 11 figures, ancillary file, RevTe
Pure Gravities via Color-Kinematics Duality for Fundamental Matter
We give a prescription for the computation of loop-level scattering
amplitudes in pure Einstein gravity, and four-dimensional pure supergravities,
using the color-kinematics duality. Amplitudes are constructed using double
copies of pure (super-)Yang-Mills parts and additional contributions from
double copies of fundamental matter, which are treated as ghosts. The
opposite-statistics states cancel the unwanted dilaton and axion in the bosonic
theory, as well as the extra matter supermultiplets in supergravities. As a
spinoff, we obtain a prescription for obtaining amplitudes in supergravities
with arbitrary non-self-interacting matter. As a prerequisite, we extend the
color-kinematics duality from the adjoint to the fundamental representation of
the gauge group. We explain the numerator relations that the fundamental
kinematic Lie algebra should satisfy. We give nontrivial evidence supporting
our construction using explicit tree and loop amplitudes, as well as more
general arguments.Comment: 48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal
versio
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