Showing 1 - 10 of 55 Items

Date: 2015-09-26

Creator: Stephen G. Naculich

Access: Open access

Abstract: In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for massless particles in gauge theory and gravity can be expressed as rational functions of the Lorentz invariants ka · kb, ϵa · kb, and ϵa · ϵb, valid in any number of spacetime dimensions. We use dimensional reduction of higher-dimensional amplitudes of particles with internal momentum κ to obtain amplitudes for massive particles in lower dimensions. In the case of gauge theory, we argue that these massive amplitudes belong to a theory in which the gauge symmetry is spontaneously broken by an adjoint Higgs field. Consequently, we show that tree-level n-point amplitudes containing massive vector and scalar bosons in this theory can be obtained by simply replacing ka · kb with ka · kb − κaκb in the corresponding massless amplitudes, where the masses of the particles are given by |κa|.

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.

Date: 1995-01-01

Creator: Stephen G. Naculich

Access: Open access

Z strings in the Weinberg-Salam model including fermions are unstable for all values of the parameters. The cause of this instability is the fermion vacuum energy in the Z-string background. Z strings with nonzero fermion densities, however, may still be stable. © 1995 The American Physical Society.

Date: 1998-12-21

Creator: Isabel P. Ennes, Stephen G. Naculich, Henric Rhedin, Howard J. Schnitzer

Access: Open access

One-instanton predictions are obtained from certain non-hyperelliptic Seiberg-Witten curves derived from M-theory for N = 2 supersymmetric gauge theories. We consider SU(N1) × SU(N2) gauge theory with a hypermultiplet in the bifundamental representation together with hypermultiplets in the defining representations of SU(N1) and SU(N2). We also consider SU(N) gauge theory with a hypermultiplet in the symmetric or antisymmetric representation, together with hypermultiplets in the defining representation. The systematic perturbation expansion about a hyperelliptic curve together with the judicious use of an involution map for the curve of the product groups provide the principal tools of the calculations. © 1999 Elsevier Science B.V.

Date: 2021-02-01

Creator: Stephen G. Naculich

Access: Open access

We examine in detail the structure of the Regge limit of the (nonplanar) N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through O(ϵ 2) at two loops, and through O(ϵ) at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the N = 8 supergravity four-point amplitude.

Date: 2018-03-01

Creator: Robert W. Brown, Stephen G. Naculich

Access: Open access

Color-factor symmetry is used to derive a KLT-type relation for tree-level QCD amplitudes containing gluons and an arbitrary number of massive or massless quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes originally postulated by Bern, De Freitas, and Wong. An explicit expression is given for all amplitudes with two or fewer quark-antiquark pairs in terms of the (modified) momentum kernel. We also introduce the bicolor scalar theory, the “zeroth copy” of QCD, containing massless biadjoint scalars and massive bifundamental scalars, generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.

Date: 2012-05-21

Creator: Alexander C. Edison, Stephen G. Naculich

Access: Open access

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=.5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations. © 2012 Elsevier B.V.

Date: 2012-01-01

Creator: Alexander C. Edison, Stephen G. Naculich

Access: Open access

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints that arise from group theory alone. These constraints break into subsets associated with irreducible representations of the symmetric group Sn, which allows them to be presented in a compact and natural way. Using an iterative approach, we derive the constraints for six-point amplitudes at all loop orders, extending earlier results for n = 4 and n = 5. We then decompose the four-, five-, and six-point group-theory constraints into their irreducible Sn subspaces. We comment briefly on higher-point two-loop amplitudes. © SISSA 2012.

Date: 2003-02-03

Creator: Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Access: Open access

We study the pp-wave limits of various elliptic models with orientifold planes and D7-branes, as well as the pp-wave limit of an orientifold of AdS5 × T11. Many of the limits contain both open and closed strings. We also present pp-wave limits of theories which give rise to a compact null direction and contain open strings. Maps between the string theory states and gauge theory operators are proposed. © 2002 Elsevier Science B.V. All rights reserved.

Date: 2007-03-13

Creator: Thomas W. Baumgarte, Stephen G. Naculich

Access: Open access

The "moving-puncture" technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving-puncture simulations, the evolution of a single black hole leads to a well-known, time-independent, maximal slicing of Schwarzschild spacetime. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example, for testing and calibrating numerical codes that employ moving-puncture techniques. In this brief report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes. © 2007 The American Physical Society.