Gauge Group Research Articles

Constraining νSMEFT coefficients: The case of the extra U(1)′

We study the constraints on low-energy coefficients of the νSMEFT generalization of the Standard Model effective theory in the simple case of a U(1)′ enlargement of the Standard Model gauge group. In particular, we analyze the constraints imposed by the requirement that the extended theory remains free of gauge anomalies. We present the cases of explicit realizations, showing the obtained correlations among the coefficients of d=6 operators. Published by the American Physical Society 2024

A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor action to a ℂℙ1 on ℂ* reduction of twistor space. Under a projection, it can be mapped to the celestial sphere at the light-cone cut of the origin on I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{I} $$\\end{document}. Geometrically, this is the common boundary celestial sphere shared by Euclidean AdS3 or Lorentzian dS3 slices of Minkowski space. We comment on the geometric meaning of the derivation from the perspective of minitwistor spaces of the 3d slices embedded in 4d Minkowski space. Using the action functional of this 2d CFT, we compute its stress-energy tensor and central charge. By a further marginal deformation, we calculate correlation functions of current algebra generators purely from the 2d side which reproduce full 4d tree-level form factors.

SU(2)L deconstruction and flavour (non)-universality

We study two-site deconstructions of the SU(2)L gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2)q × U(3)u × U(3)d flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2)ℓ or U(3)ℓ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2)L. We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C9 while naturally suppressing contributions to C10, as suggested by current b → sℓ+ℓ− data, predicting simultaneously a mild positive shift in the W boson mass.

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional 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} = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Four-loop splitting functions in QCD – The quark-to-gluon case

We present the even-N moments N≤20 of the fourth-order (N3LO) contribution Pgq(3)(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analytically computing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N≤10 derived before from structure functions in deep-inelastic scattering. Using the new moments and the available endpoint constraints, we construct approximations for Pgq(3)(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x>0.1. The resulting errors of the convolution of Pgq at N3LO with a typical quark distribution are small at x≳10−3 and exceed 1% only at x≲10−4 for a strong coupling αs=0.2. The present results for Pgq(3)(x) should thus be sufficient for most collider-physics applications.

Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential.

In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.

Vacuum structure of an eight-dimensional SU(3) gauge theory on a magnetized torus

We analyze the vacuum structure of an eight-dimensional non-Abelian gauge theory with a compactified four-dimensional torus as the extra dimensions. As a nontrivial background configuration of the gauge field of an SU(n) gauge group, we suppose a magnetic flux in two extra dimensions, and continuous Wilson line phases are also involved. We introduce matter fields and calculate the mass spectrum of low-energy modes appearing in a four-dimensional effective theory in an SU(3) model as an explicit example. As expected, potentially tachyonic states in four-dimensional modes appear from extra-dimensional gauge fields that couple to the flux background since the gauge group is simply connected. The Wilson line phases give a nonvanishing contribution to their masses, and we have a low-energy mass spectrum without tachyonic states, given that these phases take an appropriate value. To verify the validity of the values of the Wilson line phases, we examine the one-loop effective potential for these phases and explicitly show the contribution from each type of field present in our model. It is clarified that, although there seems to be no local minimum in the potential for the Wilson line phases in the pure Yang-Mills case, by including matter fields, we could find a vacuum configuration where tachyonic states disappear. Published by the American Physical Society 2024

Explaining the cosmological dark matter coincidence in asymmetric dark QCD

To properly solve the coincidence problem (ΩDM≃5ΩVM) in a model of asymmetric dark matter, one cannot simply relate the number densities of visible and dark matter without also relating their particle masses. Following previous work, we consider a framework where the dark matter is a confined state of a dark QCD gauge group whose confinement scale is dynamically related to the QCD confinement scale by a mechanism utilizing infrared fixed points of the two gauge couplings. In this work we present a new, “zero-coupling infrared fixed point” approach, which allows a larger proportion of models in this framework to generically relate the masses of the visible and dark matter particles. Due to the heavy mass scale required for the new field content, we introduce supersymmetry to the theory. We consider how these models may be incorporated in a full theory of asymmetric dark matter, presenting some example leptogenesis-like models. We also discuss the phenomenology of these models; in particular, there are gravitational wave signals which, while weak, may be measurable at future mHz and μHz detectors. Published by the American Physical Society 2024

Small instanton effects on composite axion mass

This paper investigates the impact of small instanton effects on the axion mass in composite axion models. In particular, we focus on the Composite Accidental Axion (CAA) models, which are designed to address the axion quality problem, and where the Peccei-Quinn (PQ) symmetry emerges accidentally. In the CAA models, the QCD gauge symmetry is embedded in a larger gauge group at high energy. These models contain small instantons not included in low-energy QCD, which could enhance the axion mass significantly. However, in the CAA models, our analysis reveals that these effects on the axion mass are non-vanishing but are negligible compared to the QCD effects. The suppression of the small instanton effects originates from the global chiral U(1) symmetries which are not broken spontaneously and play a crucial role in eliminating θ-terms in the hidden sectors through anomalies. We find these U(1) symmetries restrict the impact of small instantons in hidden sectors on the axion mass. Our study provides crucial insights into the dynamics within the CAA models and suggests broader implications for understanding small instanton effects in other composite axion models.

The homotopy types of SU(n)-gauge groups over $$\mathbb {C}P^3$$

The homotopy types of SU(n)-gauge groups over $$\mathbb {C}P^3$$

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Large-N integrated correlators in 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 SYM: when resurgence meets modularity

Exact expressions for certain integrated correlators of four half-BPS operators in 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 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory.

Wilson loops and random matrices

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.

Understanding the SM gauge group from SMEFT

We discuss heavy particles that can be used to pin down the faithful Standard Model (SM) gauge group and their patterns in the SM effective field theory (SMEFT). These heavy particles are not invariant under a specific ℤ6 subgroup of SU(3)c × SU(2)L × U(1)Y, which however acts trivially on all the SM particles, hence the faithful SM gauge group remains undetermined. Different realizations of the faithful SM gauge group correspond to different spectra of heavy particles, and they also correspond to distinct sets of line operators with one-form global symmetry acting on them. We show that the heavy particles not invariant under the ℤ6 group cannot appear in tree-level ultraviolet completions of SMEFT, this enforces us to consider one-loop UV completions of SMEFT to identify the ℤ6 non-invariant heavy particles. We demonstrate with examples that correlations between Wilson coefficients provide an efficient way to examine models with ℤ6 non-invariant heavy particles. Finally, we prove that all the scalars that can trigger electroweak symmetry breaking must be invariant under the ℤ6 group, hence they cannot be used to probe the faithful SM gauge group.

Probing bad theories with the dualization algorithm. Part II.

We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

Holography for Sp(2Nc) gauge dynamics: from composite Higgs to technicolour

We study Sp(2Nc) gauge dynamics with two Dirac fermion flavours in the fundamental representation. These strongly coupled systems underlie some composite Higgs models with a global symmetry breaking pattern SU(4)→Sp(4), leading to a light quartet of pseudo-Goldstone bosons that can play the role of the Higgs. Including four-fermion interactions can rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity duality, we study the underlying gauge dynamics. Our model incorporates the Nc-specific running of the fermion anomalous dimension and can thus distinguish between specific gauge groups. We determine the bound-state spectrum of the UV SU(4)→Sp(4) symmetry breaking model, also including fermion masses and mass splitting, and display the Nc dependence. The inclusion of a four-fermion interaction shows the emergence of three Goldstone bosons on the path to technicolour dynamics.

Investigation into the DNA's conformations and their conversions from the phase transition theory

The functions and transformation mechanisms of nucleic acids in their various states are of great importance in physiology and pathology. Based on the Landau model, this study reveals the mechanism of the existence of chirality and the transformation rules between different chiral conformations by studying the Duffing oscillation response of the local gauge potential on the DNA chain. The research results show that normal chiral DNA and DNA configuration transition behaviors exhibit regular nonlinear periodic oscillations. Moreover, the gauge potential value approaches zero at the B-Z junction site, which may add a criterion for detecting Z-forming sites. In addition, external force and damping play a key role in the chiral gauge potential of nucleic acids, and they can influence, regulate and even control the configuration transition of nucleic acids. Finally, we verified the rationality of our theory by combining x-ray crystal diffraction data of multiple configurations of DNA. This study provides new insights into the behavior and function of chiral DNA in organisms, and provides new possibilities for regulating DNA conformational transition in the future.

Revisiting the N=1 supersymmetric trinification models from intersecting D6-branes

We revisit the construction of the N=1 supersymmetric trinification models with gauge group U(3) C × U(3) L × U(3) R in Type IIA string theory on T6/(Z2×Z2) orientifold with intersecting D6-branes. The non-trivial K-theory conditions and tadpole cancellation conditions severely restrict the number of allowed models even for the case of rectangular two-tori. Using a supervised search algorithm, we find a few four-family models where the highest wrapping number is 2. For these models, we present the complete particle spectra and the gauge coupling relations at the string-scale.

Evolution of light deflection and shadow from a gauge-potential-like AdS black hole under the influence of a non-magnetic plasma medium

We investigate the light deflection in the weak field approximation from the accelerating charged AdS black hole. For this purpose, we apply the Gauss–Bonnet theorem to calculate the light deflection in the weak field area and use the Gibbons–Werner approach to analyze the optical geometry of the accelerating charged AdS black hole in the non-magnetic plasma absence/presence of a non-magnetic medium. We also represent the graphical behavior of the light deflection angle w.r.t. the impact parameter. We also compute the light deflection angle using Keeton and Petters approximations under the impact of accelerating charged AdS black hole geometry. Furthermore, by using the ray-tracing approach, we determine the shadow in the non-magnetic plasma presence and also demonstrate that graphical shadow has an impact on the gauge potential, non-magnetic plasma frequencies and charge.

Violation of C/CP symmetry induced by a scalar field emerging from a two-brane universe: A gateway to baryogenesis

A model of baryogenesis is introduced where our usual visible Universe is a 3-brane coevolving with a hidden 3-brane in a multidimensional bulk. The visible matter and antimatter sectors are naturally coupled with the hidden matter and antimatter sectors, breaking the C/CP invariance and leading to baryogenesis occurring after the quark-gluon era. The issue of leptogenesis is also discussed. The symmetry breaking spontaneously occurs due to the presence of an extra scalar field supported by the U(1)⊗U(1) gauge group, which extends the conventional electromagnetic gauge field in the two-brane universe. Observational consequences are discussed. Published by the American Physical Society 2024