Showing 1 - 8 of 8 Items

All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes

Date: 2013-04-19

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are mostsubleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N = 8 supergravity and mostsubleading-color N = 4 SYM amplitudes that holds for the two leading IR divergences, (Formula presented.) and (Formula presented.), but breaks down at (Formula presented.).

Linear relations between N ≥ 4 supergravity and subleading-color SYM amplitudes

Date: 2012-02-27

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

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/ε 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. © SISSA 2012.

More loops and legs in Higgs-regulated N = 4 SYM amplitudes

Date: 2010-01-01

Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin

Access: Open access

We extend the analysis of Higgs-regulated planar amplitudes of N = 4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N = 4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n ≥ 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion. © 2010 SISSA, Trieste, Italy.

One-loop SYM-supergravity relation for five-point amplitudes

Date: 2011-11-21

Creator: Stephen G. Naculich, Howard J. Schnitzer

Access: Open access

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. © 2011 SISSA.

Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: Exponentiation and Regge limits

Date: 2010-01-01

Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin

Access: Open access

We compute the three-loop contribution to the N = 4 supersymmetric Yang- Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization. © SISSA 2010.

IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM theory

Date: 2009-11-11

Creator: Stephen G. Naculich, Howard J. Schnitzer

Access: Open access

We derive a compact all-loop-order expression for the IR-divergent part of the = 4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N 2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops. © SISSA 2009.

Subleading-color contributions to gluon-gluon scattering in N = 4 SYM theory and relations to N = 8 supergravity

Date: 2008-11-01

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in = 4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of = 8 supergravity. The exact one- and two-loop = 8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent = 4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of = 4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the = 4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators. © SISSA 2008.

A super MHV vertex expansion for n=4 SYM theory

Date: 2009-07-06

Creator: Michael Kiermaier, Stephen G. Naculich

Access: Open access

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in = 4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z k falloff at (Next-to) kMHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z k+4 falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to = 8 supergravity. © SISSA 2009.