118444935
The two-loop six-point amplitude in ABJM theory
A bstractIn this paper we present the first analytic computation of the six-point two-loop amplitude of ABJM theory. We show that the two-loop amplitude consists of corrections proportional to two distinct local Yangian invariants which can be identified as the tree- and the one-loop amplitude respectively. The two-loop correction proportional to the tree-amplitude is identical to the one-loop BDS result of $ \mathcal{N}=4 $ SYM plus an additional remainder function, while the correction proportional to the one-loop amplitude is finite. Both the remainder and the finite correction are dual conformal invariant, which implies that the two-loop dual conformal anomaly equation for ABJM is again identical to that of one-loop $ \mathcal{N}=4 $ super Yang-Mills, as was first observed at four-point. We discuss the theory on the Higgs branch, showing that its amplitudes are infrared finite, but equal, in the small mass limit, to those obtained in dimensional regularization.
119182093
ABJM amplitudes and the positive orthogonal Grassmannian
A bstractA remarkable connection between perturbative scattering amplitudes of four dimensional planar SYM, and the stratification of the positive Grassmannian, was revealed in the seminal work of Arkani-Hamed et al. Similar extension for three-dimensional ABJM theory was proposed. Here we establish a direct connection between planar scattering amplitudes of ABJM theory, and singularities thereof, to the stratification of the positive orthogonal Grassmannian. In particular, scattering processes are constructed through on-shell diagrams, which are simply iterative gluing of the fundamental four-point amplitude. Each diagram is then equivalent to the merging of fundamental OG2 orthogonal Grassmannian to form a larger OGk, where 2k is the number of external particles. The invariant information that is encoded in each diagram is precisely this stratification. This information can be easily read off via permutation paths of the on-shell diagram, which also can be used to derive a canonical representation of OGk that manifests the vanishing of consecutive minors as the singularity of all on-shell diagrams. Quite remarkably, for the BCFW recursion representation of the tree-level amplitudes, the on-shell diagram manifests the presence of all physical factorization poles, as well as the cancellation of the spurious poles. After analytically continuing the orthogonal Grassmannian to split signature, we reveal that each on-shell diagram in fact resides in the positive cell of the orthogonal Grassmannian, where all minors are positive. In this language, the amplitudes of ABJM theory is simply an integral of a product of d log forms, over the positive orthogonal Grassmannian.
116887100
Color-kinematics duality for pure Yang-Mills and gravity at one and two loops
We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.
6593967
String interactions on the random lattice
Abstract We combine two partons on a random lattice as a vector state. In the ladder approximation, we find that such states have 1 / p 2 propagators (after tuning the mass to vanish). We also construct some diagrams which are very similar to 3-string vertices in string field theory for the first oscillator mode. Attaching 3 such lattice states to these vertices, we get Yang–Mills and F 3 interactions up to 3-point as from bosonic string (field) theory. This gives another view of a gauge field as a bound state in a theory whose only fundamental fields are scalars.
119118512
Worldgraph approach to Yang-Mills amplitudes from N = 2 spinning particle
By coupling the N = 2 spinning particle to background vector fields, we construct Yang-Mills amplitudes for trees and one loop. The vertex operators are derived through coupling the BRST charge; therefore background gauge invariance is manifest, and the Yang-Mills ghosts are automatically included in loop calculations by worldline ghosts. Inspired by string calculations, we extend the usual worldline approach to incorporate more ``generalized" 1D manifolds. This new approach should be useful for constructing higher-point and higher-loop amplitudes.
119283232
On three-algebra and bi-fundamental matter amplitudes and integrability of supergravity
A bstractWe explore tree-level amplitude relations for SU(N) × SU(M) bi-fundamental matter theories. Embedding the group-theory structure in a Lie three-algebra, we derive Kleiss-Kuijf-like relations for bi-fundamental matter theories in general dimension. We investigate the three-algebra color-kinematics duality for these theories. Unlike the Yang-Mills two-algebra case, the three-algebra Bern-Carrasco-Johansson relations depend on the spacetime dimension and on the detailed symmetry properties of the structure constants. We find the presence of such relations in three and two dimensions, and absence in D > 3. Surprisingly, beyond six point, such relations are absent in the Aharony-Bergman-Jafferis-Maldacena theory for general gauge group, while the Bagger-Lambert-Gustavsson theory, and its supersymmetry truncations, obey the color-kinematics duality like clockwork. At four and six points the relevant partial amplitudes of the two theories are bijectively related, explaining previous results in the literature. In D = 2 the color-kinematics duality gives results consistent with integrability of two-dimensional $ \mathcal{N} $ = 16 supergravity: the four-point amplitude satisfies a Yang-Baxter equation; the six- and eight-point amplitudes vanish for certain kinematics away from factorization channels, as expected from integrability.
118540854
Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state p = wρ
We systematically study the evolution of the Friedmann–Robertson–Walker (FRW) universe coupled with a cosmological constant Λ and a perfect fluid that has the equation of state p = wρ, where p and ρ denote, respectively, the pressure and energy density of the fluid, and w is an arbitrary real constant. Depending on the specific values of w, Λ, and the curvature k of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.
118537145
Slow-roll inflation preceded by a topological defect phase à la Chaplygin gas
We present a simple toy model corresponding to a network of frustrated topological defects of domain walls or cosmic strings that exist previous to the standard slow-roll inflationary era of the universe. Such a network (i) can produce a slower inflationary era than that of the standard scenario if it corresponds to a network of frustrated domain walls or (ii) can induce a vanishing universal acceleration; i.e., the universe would expand at a constant speed, if it corresponds to a network of frustrated cosmic strings red. Those features are phenomenologically modeled by a Chaplygin gas that can interpolate between a network of frustrated topological defects and a de Sitter-like or a power-law inflationary era. We show that this scenario can alleviate the quadruple anomaly of the cosmic microwave background spectrum. Using the method of the Bogoliubov coefficients, we obtain the spectrum of the gravitational waves as would be measured today for the whole range of frequencies. We comment on the possible detection of this spectrum by the planned detectors like BBO and DECIGO.
59329097
Stability of the de Sitter spacetime in Horava-Lifshitz theory
The stability of de Sitter spacetime in Horava–Lifshitz theory of gravity with projectability but without detailed balance condition is studied. It is found that, in contrast to the case of the Minkowski background, the spin-0 graviton is now stable for any given ξ, and free of ghost for ξ ≤ 0 in the infrared limit, where ξ is the dynamical coupling constant.
53370258
Two-particle azimuthal angle correlations and azimuthal charge balance function in relativistic heavy ion collisions
The two-particle azimuthal angle correlation (TPAC) and azimuthal charge balance function (ACBF) are used to study the anisotropic expansion in relativistic heavy ion collisions. It is demonstrated by the relativistic quantum molecular dynamics (RQMD) model and a multi-phase transport (AMPT) model that the small-angle correlation in TPAC indeed presents anisotropic expansion, and the large-angle (or back-to-back) correlation is mainly due to global momentum conservations. The AMPT model reproduces the observed TPAC, but the RQMD model fails to reproduce the strong correlations in both small and large azimuthal angles. The width of ACBF from RQMD and AMPT models decreases from peripheral to central collisions, consistent with experimental data, but in contrast to the expectation from thermal model calculations. The ACBF is insensitive to anisotropic expansion. It is a probe for the mechanism of hadronization, similar to the charge balance function in rapidity.
119118243
Stability, ghost, and strong coupling in nonrelativistic general covariant theory of gravity with $\lambda \not=1$
In this paper, we investigate three important issues: stability, ghost, and strong coupling, in the Horava-Melby-Thompson setup of the Horava-Lifshitz theory with {lambda}{ne}1, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case {lambda}=1, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton, even with {lambda}{ne}1. We also study the ghost problem in the FRW background and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes, all with the presence of matter: one is cosmological, and the other is static. We find that the coupling becomes strong for a process with energy higher than M{sub pl}|c{sub {psi}|}{sup 5/2} in the flat FRW background and M{sub pl}|c{sub {psi}|}{sup more » 3} in a static weak gravitational field, where |c{sub {psi}|{identical_to}}|(1-{lambda})/(3{lambda}-1)|{sup 1/2}. « less