arXiv subjects

Yu-tin Huang

Publications and source records attributed to Yu-tin Huang.

At least 91 records · Page 5Linked to original sources

arXiv2012

The two-loop six-point amplitude in ABJM theory

In 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 consist 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 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 N=4 SYM, 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.

hep-th↗

arXiv2012

A new integral formula for supersymmetric scattering amplitudes in three dimensions

We propose a new integral formula for all tree-level scattering amplitudes of N=6 supersymmetric Chern-Simons theory. It resembles the Roiban-Spradlin-Volovich-Witten formula for N=4 supersymmetric Yang-Mills theory based on a twistor string theory formulation. Our formula implies that the (2k)-point tree-level amplitude is closely related to degree (k-1) curves in CP^{k-1}.

hep-th↗

arXiv2012

Absence of Three-Loop Four-Point Divergences in N=4 Supergravity

We compute the coefficient of the potential three-loop divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments. The recently uncovered duality between color and kinematics is used to greatly streamline the calculation. We comment on all-loop cancellations hinting at further surprises awaiting discovery at higher loops.

hep-th↗

arXiv2012

One-loop renormalization and the S-matrix

In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the bubble coefficients captures the 1-loop UV behavior. In particular, in a renormalizable theory the sum of the bubble coefficients equals the tree-level amplitude times a proportionality constant that is related to the one-loop beta function coefficient beta_0. In this paper, we study how this proportionality is achieved from the viewpoint of on-shell amplitudes. For n-point MHV amplitude in (super) Yang-Mills theory, we demonstrate the existence of a hidden structure in each individual bubble coefficient which directly leads to systematic cancellations within the sum of them. The origin of this structure can be attributed to the collinear poles within a two-particle cut. Due to the cancellation, the one-loop beta function coefficient can be identified as a sum over the residues of unique collinear poles in particular two-particle cuts. Using CSW recursion relations, we verify the generality of this statement by reproducing the correct proportionality factor from such cuts for n-point split-helicity N^kMHV amplitudes.

hep-th↗

arXiv2012

Amplitudes for Multiple M5 Branes

We study N=(m,0) super-Poincare invariant six-dimensional massless and five-dimensional massive on-shell amplitudes. We demonstrate that in six dimensions, all possible three-point amplitudes involving tensor multiplets are necessarily embedded in gravitational theories. For non-gravitational amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0) supersymmetry, aiming at describing the world volume theory of multiple M5 branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose on-shell degrees of freedom are shown to match those of the massive particle states that arise from self-dual strings wrapping a circle. Along the way we find interesting hints of a fermionic symmetry in the (2,0) theory, which accompanies the self-dual tensor gauge symmetry. We also discuss novel theories with (3,0) and (4,0) supersymmetry.

hep-th↗

arXiv2011

Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory

In this paper we study the one- and two-loop corrections to the four-point amplitude of N=6 Chern-Simons matter theory. Using generalized unitarity methods we express the one- and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the two-loop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N=4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals.

hep-th↗

arXiv2011

Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.

hep-th↗

arXiv2011

Non-Chiral S-Matrix of N=4 Super Yang-Mills

We discuss the construction of non-chiral S-matrix of four-dimensional N=4 super Yang-Mills using a non-chiral superspace. This construction utilizes the non-chiral representation of dual superconformal symmetry, which is the natural representation from the point of view of the six-dimensional parent theory. The superspace in discussion is projective superspace constructed by Hatsuda and Siegel, and is based on a half coset U(2,2|4)/U(1,1|2)^2_+. We obtain the non-chiral representation of the five-point and general n-point MHV and anti-MHV amplitude. The non-chiral formulation can be straightforwardly lifted to six dimensions, which is equivalent to massive amplitudes in four dimensions.

hep-th↗

arXiv2011

Basics of Generalized Unitarity

We review generalized unitarity as a means for obtaining loop amplitudes from on-shell tree amplitudes. The method is generally applicable to both supersymmetric and non-supersymmetric amplitudes, including non-planar contributions. Here we focus mainly on N=4 Yang-Mills theory, in the context of on-shell superspaces. Given the need for regularization at loop level, we also review a six-dimensional helicity-based superspace formalism and its application to dimensional and massive regularizations. An important feature of the unitarity method is that it offers a means for carrying over any identified tree-level property of on-shell amplitudes to loop level, though sometimes in a modified form. We illustrate this with examples of dual conformal symmetry and a recently discovered duality between color and kinematics.

hep-th↗

arXiv2011

On-shell superamplitudes in N<4 SYM

We present an on-shell formalism for superamplitudes of pure N<4 super Yang-Mills theory. Two superfields, Phi and Phi^+, are required to describe the two CPT conjugate supermultiplets. Simple truncation prescriptions allow us to derive explicit tree-level MHV and NMHV superamplitudes with N-fold SUSY. Any N=0,1,2 tree superamplitudes have large-z falloffs under super-BCFW shifts, except under [Phi,Phi^+>-shifts. We show that this `bad' shift is responsible for the bubble contributions to 1-loop amplitudes in N=0,1,2 SYM. We evaluate the MHV bubble coefficients in a manifestly supersymmetric form and demonstrate for the case of four external particles that the sum of bubble coefficients is equal to minus the tree superamplitude times the 1-loop beta-function coefficient. The connection to the beta-function is expected since only bubble integrals capture UV divergences; we discuss briefly how the minus sign arises from UV and IR divergences in dimensional regularization. Other applications of the on-shell formalism include a solution to the N^{K}MHV N=1 SUSY Ward identities and a clear description of the connection between 6d superamplitudes and the 4d ones for both N=4 and N=2 SYM. We outline extensions to N<8 supergravity.

hep-th↗

arXiv2010

Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes

We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills theory in six dimensions, when stripped of their overall momentum and supermomentum delta functions, are covariant with respect to the six-dimensional dual conformal group. Using the generalized unitarity method, we demonstrate that this property is also present for loop amplitudes. Since the six-dimensional amplitudes can be interpreted as massive four-dimensional ones, this implies that the six-dimensional symmetry is also present in the massively regulated four-dimensional maximal super-Yang-Mills amplitudes.

hep-th↗

arXiv2010

Dual Superconformal Symmetry of N=6 Chern-Simons Theory

We demonstrate that the four and six-point tree-level amplitudes of N=6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.

hep-th↗

arXiv2010

Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space

We use supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions. In both cases, the constraints of superconformal invariance and rationality imply that the three-point amplitude vanishes on-shell, which constrains the four-point amplitude to have vanishing residues in all channels. In three dimensions, we find a unique solution for the four-point amplitude and demonstrate that it agrees with the component result in the BLG theory. This suggests that BLG is the unique three-dimensional theory with classical OSp(8|4) symmetry that admits a Lagrangian description. We also show that one can derive the four-point amplitude of the ABJM theory from our N=8 result by reducing the supersymmetry, which implies that the tree-level Yangian symmetry recently found in ABJM is also present in BLG. In six dimensions, we find that the consistency conditions imply that all tree-level amplitudes vanish. This leads us to conjecture that an interacting six-dimensional theory with classical OSp(8|4) symmetry does not have a Lagrangian description, local or nonlocal, unless the (2,0) tensor multiplets are supplemented by additional degrees of freedom.

hep-th↗

arXiv2010

Generalized Unitarity and Six-Dimensional Helicity

We combine the unitarity method with the six-dimensional helicity formalism of Cheung and O'Connell to construct loop-level scattering amplitudes. As a first example, we construct dimensionally regularized QCD one-loop four-point amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions less than or equal to six. We comment on the connection of our approach to the recently discussed Higgs infrared regulator and on dual conformal properties in six dimensions.

hep-th↗

arXiv2010

Supertwistor space for 6D maximal super Yang-Mills

6D maximal super Yang-Mills on-shell amplitudes are formulated in superspace using 6 dimensional twistors. The 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction. In contrast to 4D this superspace is non-chiral, reflecting the fact that one cannot differentiate MHV from $\bar{\rm MHV}$ in 6D. Combined with unitarity methods, this superspace should be useful for the study of multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes. Furthermore, the non-chiral nature gives a natural framework for an off-shell construction. We show this by matching our result with off-shell D=4 N=4 super Yang-Mills amplitudes, expressed in projective superspace.

hep-th↗

arXiv2010

Gravity as the Square of Gauge Theory

We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By "squaring" the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.

hep-th↗

arXiv2009

MHV Lagrangian for N=4 Super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\barΛ\bar{\rm A}Λ{\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.

hep-th↗

arXiv2009

First-quantized N=4 Yang-Mills

We present simple first-class-constraint actions and BRST operators for the 4D N=4 superparticle. Each generation of ghosts has 2 super-indices, like the coordinates. The constraints that define projective superspace close in a super Yang-Mills background due to the presence of a (non-central) U(1) generator in the algebra.

hep-th↗