Showing 1 - 5 of 5 Items
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.
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.).
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.
Applications of subleading-color amplitudes in N = 4 SYM theory
Date: 2011-12-01
Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer
Access: Open access
- A number of features and applications of subleading-color amplitudes of N = 4 SYM theory are reviewed. Particular attention is given to the IR divergences of the subleading-color amplitudes, the relationships of N = 4 SYM theory to N = 8 supergravity, and to geometric interpretations of one-loop subleading-color and N k MHV amplitudes of N = 4 SYM theory. Copyright © 2011 Stephen G. Naculich et al.
Two-loop graviton scattering relation and IR behavior in N = 8 supergravity
Date: 2008-12-11
Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer
Access: Open access
- We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N = 8 supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms. © 2008 Elsevier B.V. All rights reserved.