Maximally Helicity Violating Research Articles

No U(1) ‘electric-magnetic’ duality in Einstein gravity

We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.

All-order celestial OPE from on-shell recursion

We determine tree level, all-order celestial operator product expansions (OPEs) of gluons and gravitons in the maximally helicity violating (MHV) sector. We start by obtaining the all-order collinear expansions of MHV amplitudes using the inverse soft recursion relations that they satisfy. These collinear expansions are recast as celestial OPE expansions in bases of momentum as well as boost eigenstates. This shows that inverse soft recursion for MHV amplitudes is dual to OPE recursion in celestial conformal field theory.

An eight loop amplitude via antipodal duality

We compute the six-particle maximally-helicity-violating (MHV) amplitude in planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills theory at eight loops, using antipodal duality and the recently computed eight-loop three-point form factor for the chiral stress energy tensor multiplet. Antipodal duality maps the form factor symbol to the amplitude symbol on a two-dimensional parity-preserving surface in the three-dimensional amplitude kinematics. There are remarkably few ambiguities in lifting from two to three dimensions, nor in promoting the symbol to a function. The amplitude passes many tests, including near-collinear, multi-Regge, factorization, self-crossing and origin limits. These checks also constitute a validation of antipodal duality at eight loops.

Constructing EYM amplitudes by inverse soft limit

It is well known that gravity amplitudes in four dimensions can be reconstructed by the inverse soft limit (ISL) method. According to ISL, a tree level n-graviton maximally-helicity-violating (MHV) amplitude is expressed in terms of deformed (n − 1)-graviton amplitudes accompanied by soft graviton factors. On another hand, single- and double-trace tree-level Einstein-Yang-Mills (EYM) MHV amplitudes have been proven to satisfy spanning forest formulas, where each edge in a forest has the same form with a term in soft graviton factor. It is not transparent that the formulas satisfied by EYM amplitudes can be constructed with ISL. In this paper, we construct the single- and double-trace MHV amplitudes in EYM, by the ISL and show that the known formulas can be precisely reproduced. Interesting identities which are based on Schouten identity and characterized by graphs are also introduced.

Higher-spin Yang–Mills, amplitudes and self-duality

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude.

All-order celestial OPE in the MHV sector

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

A note on multi-trace EYM amplitudes in four dimensions

In four dimensions, a tree-level double-trace Einstein-Yang-Mills (EYM) amplitude with two negative-helicity gluons (the (g−, g−)-configuration) satisfies a symmetric spanning forest formula, which was derived from the graphic expansion rule. On another hand, in the framework of Cachazo-He-Yuan (CHY) formula, the maximally-helicity-violating (MHV) amplitudes are supported by the MHV solution of scattering equations. The relationship between the symmetric formula for double-trace amplitudes, and the MHV sector of Cachazo-He-Yuan (CHY) formula in four dimensions is still not clear. In this note, we promote a series of transformations of the spanning forests in four dimensions and then show a systematic way for decomposing the MHV sector of the CHY formula of double-trace EYM amplitudes. Along this line, the symmetric formula of double-trace MHV amplitudes is directly obtained by the MHV sector of CHY formula. We then prove that EYM amplitude with an arbitrary total number of negative-helicity particles (gravitons and gluons) has to vanish when the number of negative- (or positive-) helicity gluons is less than the number of traces.

Feynman Integrals and Scattering Amplitudes from Wilson Loops.

We study Feynman integrals and scattering amplitudes in N=4 super-Yang-Mills theory by exploiting the duality with null polygonal Wilson loops. As the main application, we compute for the first time the symbols of the general double pentagon integrals, which give the finite part of two-loop maximally helicity violating (MHV) amplitudes and finite components of next-to-MHV (NMHV) amplitudes to all multiplicities. The rational parts of the symbol consist of 164 letters, while the algebraic part contains 96 algebraic letters and cancel in MHV amplitudes and NMHV components which are free of square roots.

How tropical are seven- and eight-particle amplitudes?

We study tropical Grassmanians Tr(k, n) in relation to cluster algebras, and assess their applicability to n-particle amplitudes for n = 7, 8. In mathcal{N} = 4 super Yang-Mills theory, we first show that while the totally positive part of Tr(4, 7) may encompass the iterated discontinuity structure of the seven-point Maximally Helicity Violating (MHV) amplitude, it is too small for the Next-to-MHV helicity configuration. Then, using Tr(4, 8) we propose a finite set of 356 cluster mathcal{A} -coordinates expected to contain the rational symbol letters of the eight-particle MHV amplitude, and discuss how the remaining square-root letters may be obtained from limits of infinite mutation sequences. Finally, we use a triangulation of the totally positive part of Tr(3, 8) to obtain the associated generalised biadjoint scalar amplitude in a form containing a near-minimal amount of spurious poles.

Maximal-Helicity-Violating Scattering of Gluons and Gravitons in Chiral Strong Fields.

We present all-multiplicity formulas for the tree-level scattering of gluons and gravitons in the maximal helicity violating (MHV) helicity configuration, calculated in certain chiral strong fields. The strong backgrounds we consider are self-dual plane waves in gauge theory and general relativity, which are treated exactly and admit a well-defined S matrix. The gauge theory background-coupled MHV amplitude is simply a dressed analog of the familiar Parke-Taylor formula, but the gravitational version has nontrivial new structures due to graviton tails. Both formulas have just one residual integral rather than the n-2 expected at n points from space-time perturbation theory; this simplification arises from the integrability of self-dual backgrounds and their corresponding twistor description. The resulting formulas pass several consistency checks and limit to the well-known expressions for MHV scattering of gluons and gravitons when the background becomes trivial.

D3-brane loop amplitudes from M5-brane tree amplitudes

We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory. We show that the D3-brane loop superamplitudes can be obtained from the tree-level superamplitudes in the world-volume theory of a probe M5-brane (or D5-brane). The M5-brane theory describes self-interactions of an abelian tensor supermultiplet with (2, 0) supersymmetry, and the tree-level superamplitudes are given by a twistor formula. We apply the construction to the maximally-helicity-violating (MHV) amplitudes in the D3- brane theory at one-loop order, which are purely rational terms (except for the four-point amplitude). The results are further confirmed by generalised unitarity methods. Through a supersymmetry reduction on the M5-brane tree-level superamplitudes, we also construct one-loop corrections to the non-supersymmetric D3-brane amplitudes, which agree with the known results in the literature.

Multi-Biometric System Based on Cutting-Edge Equipment for Experimental Contactless Verification

Biometric verification methods have gained significant popularity in recent times, which has brought about their extensive usage. In light of theoretical evidence surrounding the development of biometric verification, we proposed an experimental multi-biometric system for laboratory testing. First, the proposed system was designed such that it was able to identify and verify a user through the hand contour, and blood flow (blood stream) at the upper part of the hand. Next, we detailed the hard and software solutions for the system. A total of 40 subjects agreed to be a part of data generation team, which produced 280 hand images. The core of this paper lies in evaluating individual metrics, which are functions of frequency comparison of the double type faults with the EER (Equal Error Rate) values. The lowest value was measured for the case of the modified Hausdorff distance metric - Maximally Helicity Violating (MHV). Furthermore, for the verified biometric characteristics (Hamming distance and MHV), appropriate and suitable metrics have been proposed and experimented to optimize system precision. Thus, the EER value for the designed multi-biometric system in the context of this work was found to be 5%, which proves that metrics consolidation increases the precision of the multi-biometric system. Algorithms used for the proposed multi-biometric device shows that the individual metrics exhibit significant accuracy but perform better on consolidation, with a few shortcomings.

Six-Gluon amplitudes in planar mathcal{N} = 4 super-Yang-Mills theory at six and seven loops

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

All-loop cuts from the Amplituhedron

The definition of the amplituhedron in terms of sign flips involves both one-loop constraints and the “mutual positivity” constraint. To gain an understanding of the all-loop integrand of mathcal{N}=4 sYM requires understanding the crucial role played by mutual positivity. This paper is an attempt towards developing a procedure to introduce the complexities of mutual positivity in a systematic and controlled manner. As the first step in this procedure, we trivialize these constraints and understand the geometry underlying the remaining constraints to all loops and multiplicities. We present a host of configurations which correspond to various faces of the amplituhedron. The results we derive are valid at all multiplicities and loop orders for the maximally helicity violating (MHV) configurations. These include detailed derivations for the results in [1]. We conclude by indicating how one might move beyond trivial mutual positivity by presenting a series of configuration which re-introduce it bit by bit.

Minitwistors and 3d Yang-Mills-Higgs theory

We construct a minitwistor action for Yang–Mills–Higgs (YMH) theory in three dimensions. The Feynman diagrams of this action will construct perturbation theory around solutions of the Bogomolny equations in much the same way that MHV (maximally helicity violating) diagrams describe perturbation theory around the self-dual Yang Mills equations in four dimensions. We also provide a new formula for all tree amplitudes in YMH theory (and its maximally supersymmetric extension) in terms of degree d maps to minitwistor space. We demonstrate its relationship to the Roiban-Spradlin-Volovich-Witten (RSVW) formula in four dimensions and show that it generates the correct MHV amplitudes at d = 1 and factorizes correctly in all channels for all degrees.

MHV amplitudes at strong coupling and linearized TBA equations

The maximally helicity violating (MHV) amplitudes of mathcal{N}=4 super Yang-Mills theory at strong coupling are obtained by solving auxiliary thermodynamic Bethe ansatz (TBA) integral equations. We consider a limit where the TBA equations are linearized for large chemical potentials and masses therein. By solving the linearized equations, we derive analytic expansions of the 6-point MHV amplitudes in terms of the ratio of the chemical potential A and the mass M . The expansions are valid up to corrections exponentially small in A or inversely proportional to powers of A. The analytic expansions describe the amplitudes for small conformal cross-ratios of the particle momenta in a standard basis, and interpolate the amplitudes with equal cross-ratios and those in soft/collinear limits. The leading power corrections are also obtained analytically. We compare the 6-point rescaled remainder functions at strong coupling and at 2 loops for the above kinematics. They are rather different, in contrast to other kinematic regions discussed in the literature where they are found to be similar to each other.

Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in mathcal{N}=2 super-Yang-Mills (SYM) theory coupled to Nf fundamental hypermultiplets. Our results are valid in D ≤ 6 dimensions, where the upper bound corresponds to six-dimensional chiral mathcal{N}=left(1,0right) SYM theory. By exploiting a close connection with mathcal{N}=4 SYM theory — and, equivalently, six-dimensional mathcal{N}=left(1,1right) SYM theory — we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding D-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning Nf enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in D = 4. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with mathcal{N}=left(1,1right) and mathcal{N}=left(2,0right) supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in D = 5 − 2ϵ and show that it non-trivially cancels out as expected.

Computing the qg → qg cross section using the BCFW recursion and introduction to jet tomography in heavy ion collisions via MHV techniques

To make predictions for the particle physics processes, one has to compute the cross section of the specific process as this is what one can measure in a modern collider experiment such as the Large Hadron Collider (LHC) at CERN. Theoretically, it has been proven to be extremely difficult to compute scattering amplitudes using conventional methods of Feynman. Calculations with Feynman diagrams are realizations of a perturbative expansion and when doing calculations one has to set up all topologically different diagrams, for a given process up to a given order of coupling in the theory. This quickly makes the calculation of scattering amplitudes a hot mess. Fortunately, one can simplify calculations by considering the helicity amplitude for the Maximally Helicity Violating (MHV). This can be extended to the formalism of on-shell recursion, which is able to derive, in a much simpler way the expression of a high order scattering amplitude from lower orders.

Correction to the Probability Distribution of Induced Gluon

We present a novel technique for the calculation of the probability for emission of gluon radiated from a high-pT quark through a medium (QGP). Our work is an extension of the maximal helicity violating (MHV) method to compute the non-abelian correction for 2 gluon emissions.

Beyond the Poisson Approximation: n-gluon radiation in QGP

We present a novel technique for the calculation of the probability for emission of gluon radiated from a high-pT quark through a medium (QGP). Our work is an extension of the maximal helicity violating (MHV) method in which the usual soft-collinear factor is classified according to its symmetry under gluon permutation. For the purposes of illustration, we show the result from 1 to 3 gluon radiation.