skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
A<sc>bstract</sc> In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop orderL) 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 ofN). Using an iterative process, we systematically construct theL-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 (forL≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (forL≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.  more » « less
Award ID(s):
2111943
PAR ID:
10552815
Author(s) / Creator(s):
;
Publisher / Repository:
Published for SISSA by Springer
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2024
Issue:
10
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of High Energy Physics)
    We describe a novel variation of the mirror twin Higgs model in which the color gauge group in both sectors is extended to SU(4)cand spontaneously broken to SU(3)cexclusively in the visible sector. Through this process, the mirrorZ2symmetry is spontaneously broken, allowing for a phenomenologically viable electroweak vacuum alignment. This structure produces interesting collider signatures, including heavy vectors and fermions with fractional electric charges. The twin sector, with unbroken SU(4)c, produces interesting cosmological characteristics, such as the possibility to reduce ∆Neffand stable spin-0 baryons. The enlarged top quark sector required by the extended color gauge symmetry preserves naturalness, with even less tuning than the original twin Higgs in many circumstances. 
    more » « less
  2. ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants). 
    more » « less
  3. ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colorsN. In this note we compare the largeNlattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with$$ \mathcal{N} $$ N = 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with largeNthe lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2++and 1−−mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories. 
    more » « less
  4. ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> In [1], logarithmic correction to subleading soft photon and soft graviton theorems have been derived in four spacetime dimensions from the ratio of IR-finite S-matrices. This has been achieved after factoring out IR-divergent components from the traditional electromagnetic and gravitational S-matrices using Grammer-Yennie prescription. Although the loop corrected subleading soft theorems are derived from one-loop scattering amplitudes involving scalar particles in a minimally coupled theory with scalar contact interaction, it has been conjectured that the soft factors are universal (theory independent) and one-loop exact (don’t receive corrections from higher loops). This paper extends the analysis conducted in [1] to encompass general spinning particle scattering with non-minimal couplings permitted by gauge invariance and general coordinate invariance. By re-deriving the lnωsoft factors in this generic setup, we establish their universal nature. Furthermore, we summarize the results of loop corrected soft photon and graviton theorems up to sub-subleading order, which follows from the analysis of one and two loop QED and quantum gravity S-matrices. While the classical versions of these soft factors have already been derived in the literature, we put forth conjectures regarding the quantum soft factors and outline potential strategies for their derivation. 
    more » « less
  5. ; ; ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> We analyze correlation functions of SU(k) × SU(2)Fflavor currents in a family of three-dimensional$$ \mathcal{N} $$ N = 4 superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on AdS4×S7/ℤkwhich contains a ℂ2/ℤkorbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator from the combined contribution of two-loop gluon and tree-level bulk graviton exchange. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email