Stephen G. Naculich
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Stephen G. Naculich has a total of 108 co-authors. Here are the top co-authors by number of shared publications:
Howard J. Schnitzer
Theoretical Physics Group, Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA
29 shared publications- Howard J. Schnitzer
Brandeis University
24 shared publications - Howard J. Schnitzer
Martin Fisher School of Physics Brandeis University 02454 Waltham MA
12 shared publications - Howard J. Schnitzer
Martin Fisher School of Physics
9 shared publications Niclas Wyllard
8 shared publications- Niclas Wyllard
Martin Fisher School of Physics Brandeis University 02454 Waltham MA
8 shared publications
Latest Publications
- Open Access
- 7 October 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (10) , 72
Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
A bstract: Bern-Carrasco-Johansson relations are helicity-independent constraints among the partial amplitudes of tree-level processes containing gluons and possibly also matter fields. They are a consequence of color-kinematic duality, but alternatively can be derived using the color-factor symmetry of tree-level amplitudes. We use recursive perturbiner methods to present a general, streamlined proof of the color-factor symmetry of all tree-level amplitudes containing an arbitrary number of fundamental spin-zero or spin-one-half matter fields and at least one gluon.
- 7 October 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (10) , 72
Open AccessColor-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
A bstract: Bern-Carrasco-Johansson relations are helicity-independent constraints among the partial amplitudes of tree-level processes containing gluons and possibly also matter fields. They are a consequence of color-kinematic duality, but alternatively can be derived using the color-factor symmetry of tree-level amplitudes. We use recursive perturbiner methods to present a general, streamlined proof of the color-factor symmetry of all tree-level amplitudes containing an arbitrary number of fundamental spin-zero or spin-one-half matter fields and at least one gluon.
- Open Access
- 30 October 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (10) , 1-43
All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an iterative process, we systematically construct the L-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (for L ≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (for L ≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.
- 30 October 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (10) , 1-43
Open AccessAll-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an iterative process, we systematically construct the L-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (for L ≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (for L ≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.
- Open Access
Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion.
Open AccessColor-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion.
- Open Access
- 15 June 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (6) , 1-20
Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion.
- 15 June 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (6) , 1-20
Open AccessColor-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion.
- Open Access
Proof of a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity
A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.
Open AccessProof of a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity
A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.
- Open Access
- 7 July 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (7) , 1-29
Proof of a three-loop relation between the Regge limits of four-point amplitudes in $ \mathcal{N} $ = 4 SYM and $ \mathcal{N} $ = 8 supergravityA previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory and $$ \mathcal{N} $$ = 8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.- 7 July 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (7) , 1-29
Open AccessProof of a three-loop relation between the Regge limits of four-point amplitudes in $ \mathcal{N} $ = 4 SYM and $ \mathcal{N} $ = 8 supergravityA previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory and $$ \mathcal{N} $$ = 8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered. - Open Access
- 4 February 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (2) , 1-32
All-loop-orders relation between Regge limits of $ \mathcal{N} $ = 4 SYM and $ \mathcal{N} $ = 8 supergravity four-point amplitudesWe examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ = 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 $$ \mathcal{O}\left({\upepsilon}^2\right) $$ at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ 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 $$ \mathcal{N} $$ = 8 supergravity four-point amplitude.- 4 February 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (2) , 1-32
Open AccessAll-loop-orders relation between Regge limits of $ \mathcal{N} $ = 4 SYM and $ \mathcal{N} $ = 8 supergravity four-point amplitudesWe examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ = 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 $$ \mathcal{O}\left({\upepsilon}^2\right) $$ at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ 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 $$ \mathcal{N} $$ = 8 supergravity four-point amplitude. - Open AccessAll-loop-orders relation between Regge limits of ${\cal N}=4$ SYM and ${\cal N}=8$ supergravity four-point amplitudesWe examine in detail the structure of the Regge limit of the (nonplanar) ${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color factors $C_{ik}$ 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 ${\cal O} (\epsilon^2)$ at two loops, and through ${\cal O} (\epsilon^0)$ 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 ${\cal N} =8$ supergravity four-point amplitude.Open AccessAll-loop-orders relation between Regge limits of ${\cal N}=4$ SYM and ${\cal N}=8$ supergravity four-point amplitudesWe examine in detail the structure of the Regge limit of the (nonplanar) ${\cal N}=4$ SYM four-point amplitude. We begin by developing a basis of color factors $C_{ik}$ 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 ${\cal O} (\epsilon^2)$ at two loops, and through ${\cal O} (\epsilon^0)$ 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 ${\cal N} =8$ supergravity four-point amplitude.
- Open Access
- 30 March 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (3) , 1-35
A tale of two exponentiations in $ \mathcal{N} $ = 8 supergravity at subleading levelHigh-energy massless gravitational scattering in $$ \mathcal{N} $$ = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.- 30 March 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (3) , 1-35
Open AccessA tale of two exponentiations in $ \mathcal{N} $ = 8 supergravity at subleading levelHigh-energy massless gravitational scattering in $$ \mathcal{N} $$ = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation. - Open AccessA tale of two exponentiations in ${\cal N}=8$ supergravity at subleading levelHigh-energy massless gravitational scattering in ${\cal N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $\epsilon$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.Open AccessA tale of two exponentiations in ${\cal N}=8$ supergravity at subleading levelHigh-energy massless gravitational scattering in ${\cal N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $\epsilon$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.