Weak Gauge Coupling Research Articles

The gauge coupling evolutions of an SU(8) theory with the maximally symmetry breaking pattern

We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an SU(8) theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate the observed SM quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern through its maximally breaking pattern. The field theoretical two-loop RGEs can not achieve the gauge coupling unification with the minimal setup, unless additional adjoint Higgs fields as well as the gravity-induced d = 5 term to the SU(8) field strength term are included.

Decoding stringy near-supersymmetric black holes

Building on the recent discovery of the first candidate black hole operator in the \mathcal{N}=4𝒩=4 super-Yang-Mills, we explore the near-supersymmetric aspects of the theory that capture lightly excited, highly stringy black holes. We extend the superspace formalism describing the classically supersymmetric (1/16-BPS) sector of \mathcal{N}=4𝒩=4 super-Yang-Mills and compute a large number of one-loop anomalous dimensions. Despite being in the highly stringy regime, we find hints of a gap in the spectrum, similar to that found by a gravitational path integral. We also determine the actual expression of the first candidate black hole operator at weak gauge coupling, going beyond the cohomological construction.

Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation

According to the preceding studies, the lattice SU(2) gauge-scalar model with a single scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase where confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamic phase transitions, which is a well-known consequence of the Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, we show that we can define new types of gauge-invariant operators by combining the original fundamental scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. By performing the numerical simulations on the lattice without any gauge fixing, we reproduce the conventional thermodynamic transition line in the weak gauge coupling, and moreover we find a new transition line detected by the new gauge-invariant operators which separates the confinement-Higgs phase into two parts, confinement phase and the Higgs phase, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we discuss a physical interpretation for the new transition from the viewpoint of the realization of a global symmetry. Published by the American Physical Society 2024

Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry

Abstract We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the Dp-brane solution. The string-frame metric is AdSp + 2 × S8 − p times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S8 − p. In this paper, we extend this result to operators that have angular momenta along AdSp + 2. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665, 94 (2003)] and on the “string bit” picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636, 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced.

Are low-energy data already hinting at five dimensions?

Low-energy data, combined with renormalization group (RG) equations, can predict new physics at far higher energy scales. In this paper, we consider the possibility that the measured Higgs boson mass and top quark mass hint at a five-dimensional gauge-Higgs unification (5D GHU) model at a scale above TeV. We note that the vanishing of the Higgs quartic coupling and the proximity of the top quark Yukawa coupling and weak gauge coupling at high scales, inferred from the experimental data, are in harmony with 5D GHU, because in 5D GHU models the Higgs quartic coupling is forbidden by the 5D gauge symmetry and the Yukawa couplings and the weak gauge coupling originate from a common 5D gauge coupling. Based on the above insight, we propose a 5D GHU model where the Standard Model fermions are embedded in 5D fermions in a way to tightly relate the top Yukawa coupling with the weak gauge coupling. Also, the model predicts the presence of vector-like fermions (other than the Kaluza-Klein modes), which can affect the RG evolutions of the 4D theory and reconcile the scale of vanishing Higgs quartic coupling and that of equality of the top Yukawa and weak gauge couplings, thereby achieving a successful matching of the 4D theory with 5D GHU. We predict the vector-like fermion mass and the compactification scale of 5D GHU from the conditions for the successful matching.

Supersymmetry breaking deformations and phase transitions in five dimensions

We analyze a recently proposed supersymmetry breaking mass deformation of the E1 superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure SU(2) Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.

Ising model as a U(1) lattice gauge theory with a θ -term

We discuss a gauged XY model a $\theta$-term on an arbitrary lattice in 1+1 dimensions, and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the topological term is defined via the Villain action. We discuss the phase diagram by comparing the strong and weak gauge coupling limits, and perform Monte Carlo simulations at intermediate couplings. We generalize the duality to higher-dimensional Ising models using higher-form U(1) gauge field analogues.

Scrutinizing vacuum stability in IDM with Type-III inverse seesaw

We consider the extension of the Standard Model (SM) with an inert Higgs doublet that also contains two or three sets of SU(2)L triplet fermions with hypercharge zero and analyze the stability of electroweak vacuum for the scenarios. The model represents a Type-III inverse seesaw mechanism for neutrino mass generation with a Dark matter candidate. An effective potential approach calculation with two-loop beta function have been carried out in deciding the fate of the electroweak vacuum. Weak gauge coupling g2 shows a different behaviour as compared to the Standard Model. The modified running of g2, along with the Higgs quartic coupling and Type-III Yukawa couplings become crucial in determining the stability of electroweak vacuum. The interplay between two and three generations of such triplet fermions reveals that extensions with two generations is favoured if we aspire for Planck scale stability. Bounds on the Higgs quartic couplings, Type-III Yukawa and number of triplet fermion generations are drawn for different mass scale of Type-III fermions. The phenomenologies of inert doublet and Type-III fermions at the LHC and other experiments are commented upon.

Tricritical points in a compactU(1)lattice gauge theory at strong coupling

Pure {\it compact} $U(1)$ lattice gauge theory exhibits a phase transition at gauge coupling $g \sim {\cal{O}}(1)$ separating a familiar weak coupling Coulomb phase, having free massless photons, from a strong coupling phase. However, the phase transition was found to be of first order, ruling out any nontrivial theory resulting from a continuum limit from the strong coupling side. In this work, a compact $U(1)$ lattice gauge theory is studied with addition of a dimension-two mass counterterm and a higher derivative (HD) term that ensures a unique vacuum and produces a covariant gauge-fixing term in the naive continuum limit. For a reasonably large coefficient of the HD term, now there exists a continuous transition from a regular ordered phase to a spatially modulated ordered phase. For weak gauge couplings, a continuum limit from the regular ordered phase results in a familiar theory consisting of free massless photons. For strong gauge couplings with $g\ge {\cal{O}}(1)$, this transition changes from first order to continuous as the coefficient of the HD term is increased, resulting in tricritical points which appear to be a candidate in this theory for a possible nontrivial continuum limit.

Top quark spin correlations and polarization at the LHC: Standard model predictions and effects of anomalous top chromo moments

A number of top-spin observables are computed within the Standard Model (SM), at next-to-leading order in the strong and weak gauge couplings for hadronic top-quark anti-quark (tt¯) production and decay at the LHC for center-of-mass energies 7 and 8 TeV. For dileptonic final states we consider the azimuthal angle correlation, the helicity correlation, and the opening angle distribution; for lepton plus jets final states we determine distributions and asymmetries that trace a longitudinal and transverse polarization, respectively, of the t and t¯ samples. The QCD-induced transverse polarization of the top quarks leads to an asymmetry of about 8% that should be detectable with existing data. In addition, we investigate the effects of a non-zero chromo-magnetic and chromo-electric dipole moment of the top quark on these and other top-spin observables and associated asymmetries. These observables allow to disentangle the contributions from the real and imaginary parts of these moments.

Non-Abelian gauged Nambu–Jona-Lasinio models on the lattice

We use Monte Carlo simulation to probe the phase structure of a $SU(2)$ gauge theory containing ${N}_{f}$ Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional four-fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory. The resultant lattice theory is invariant under a set of shift symmetries which correspond to a discrete subgroup of the continuum chiral-flavor symmetry. The pseudoreal character of the representation guarantees that the theory has no sign problem. For the case of ${N}_{f}=4$ we observe a crossover in the behavior of the chiral condensate for strong four-fermi coupling associated with the generation of a dynamical mass for the fermions. At weak gauge coupling this crossover is consistent with the usual continuous phase transition seen in the pure (ungauged) Nambu--Jona-Lasinio model. However, if the gauge coupling is strong enough to cause confinement, we observe a much more rapid crossover in the chiral condensate consistent with a first order phase transition.

The phase and critical point of quantum Einstein–Cartan gravity

By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D 82 (2010) 064039] the quantum Einstein–Cartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein–Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein–Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.

Magnetic monopole plasma phase in(2+1)dcompact quantum electrodynamics with fermionic matter

We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED3) with N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on the divergence of the monopole susceptibility (polarizability) with the lattice size at weak gauge couplings. A weak four-Fermi term added to the cQED3 action enabled simulations with massless fermions. The exact chiral symmetry of the interaction terms forbids symmetry breaking lattice discretization counterterms to appear in the theory's effective action. It is also shown that the scenario of a monopole plasma does not depend on the strength of the four-Fermi coupling. Other observables such as the densities of "isolated" dipoles and monopoles and the so-called specific heat show that a crossover from a dense monopole plasma to a dilute monopole gas occurs at strong couplings. The implications of our results on the stability of U(1) spin liquids in two spatial dimensions are also discussed.

B-L cosmic strings in heterotic standard models

E_{8} X E_{8} heterotic string and M-theory, when compactified on smooth Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken N=1 supersymmetric theories with the exact matter spectrum of the MSSM, including three right-handed neutrinos and one Higgs-Higgs conjugate pair of supermultiplets. These vacua have the SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge group of the standard model augmented by an additional gauged U(1)_{B-L}. Their minimal content requires that the B-L symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. The soft supersymmetry breaking operators can induce radiative breaking of the B-L gauge symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is shown that U(1)_{B-L} cosmic strings occur in this context, potentially with both bosonic and fermionic superconductivity. We present a numerical analysis that demonstrates that boson condensates can, in principle, form for theories of this type. However, the weak Yukawa and gauge couplings of the right-handed sneutrino suggests that bosonic superconductivity will not occur in the simplest vacua in this context. The electroweak phase transition also disallows fermion superconductivity, although substantial bound state fermion currents can exist.

Finite energy shifts inSU(n)supersymmetric Yang-Mills theory onT3×Rat weak coupling

We consider a semi-classical treatment, in the regime of weak gauge coupling, of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we consider the theories obtained as power series expansions around a certain class of normalizable vacua of the classical theory, corresponding to isolated points in the moduli space of flat connections, and the perturbative corrections to the free energy eigenstates and eigenvalues in the weakly interacting theory. The perturbation theory construction of the interacting Hilbert space is complicated by the divergence of the norm of the interacting states. Consequently, the free and interacting Hilbert furnish unitarily inequivalent representation of the algebra of creation and annihilation operators of the quantum theory. We discuss a consistent redefinition of the Hilbert space norm to obtain the interacting Hilbert space and the properties of the interacting representation. In particular, we consider the lowest non-vanishing corrections to the free energy spectrum and discuss the crucial importance of supersymmetry for these corrections to be finite.

Distributions and correlations for top quark pair production and decay at the Tevatron and LHC

We investigate a number of observables that are and will be instrumental in the exploration of t t ¯ production and decay at the Tevatron and the LHC. For this analysis we made a computer program that incorporates besides the NLO QCD corrections to t t ¯ production and decay also mixed weak-QCD corrections to the production amplitudes, and that allows for studies of correlated versus uncorrelated t t ¯ events. In this paper we analyze and compute observables mostly for dileptonic t t ¯ final states to next-to-leading order in the strong and weak gauge couplings (NLOW), with selection cuts. We calculate charge asymmetries of the top quark and of ℓ = e , μ and we compare, where possible, with experimental results. We show that top-quark spin correlations affect a leptonic pair asymmetry (which has not been measured so far) by ∼7%. We determine several dileptonic angular correlations, which reflect t t ¯ spin correlations, namely the beam, off-diagonal and helicity correlation, and the opening angle distribution (defined in the t, t ¯ rest frames) when selection cuts are applied. Our NLOW predictions for the beam, off-diagonal, and helicity correlation for the Tevatron agree with recent measurements by the CDF and DØ experiments. In addition we make predictions for estimators of these correlations as functions of M t t ¯ . These estimators may prove useful for the Tevatron and also in the early rounds of LHC data-analyses, where the event numbers will not be abundant. Furthermore, we compute to NLOW in the gauge couplings two dilepton angular correlations that are defined in the laboratory frame, for correlated and uncorrelated t t ¯ events at the LHC. Finally, based on our SM results, we identify several observables that allow to search for non-standard parity- and CP-violating interactions, especially with future LHC data.

Moduli stabilisation in heterotic string compactifications

In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalised half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N=1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalised models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification.

Kachru-Kallosh-Linde-Trivedi-type models with moduli-mixing superpotential

We study KKLT type models with moduli-mixing superpotential. In several string models, gauge kinetic functions are written as linear combinations of two or more moduli fields. Their gluino condensation generates moduli-mixing superpotential. We assume one of moduli fields is frozen already around the string scale. It is found that K\"ahler modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on (non-)magnetized D-brane. Furthermore, we do not need to highly tune parameters in order to realize a weak gauge coupling and a large hierarchy between the gravitino mass and the Planck scale, when there exists non-perturbative effects on D3-brane. SUSY breaking patterns in our models have a rich structure. Also, some of our models have cosmologically important implications, e.g., on the overshooting problem and the destabilization problem due to finite temperature effects as well as the gravitino problem and the moduli problem.

Mixed top-bottom squark production at the CERN LHC

We calculate cross sections for mixed stop-sbottom pair production at the LHC, analogous to single-top production, a weak process involving the $W$-${\stackrel{\texttildelow{}}{t}}_{i}$-${\stackrel{\texttildelow{}}{b}}_{j}$ vertex. While coupling-suppressed relative to QCD same-flavor squark pair production, the signal is distinctive due to heavy-flavor tagging along with a possible same-sign lepton pair in the final state. SUSY backgrounds can often be suppressed many orders of magnitude by taking advantage of distinct kinematic differences from the signal. Measuring the rate of this process would add significant additional information to that gathered from other SUSY processes. If the stop and sbottom mixings can be determined elsewhere, stop-sbottom production would provide for a measurement of the weak squark gauge coupling and super-CKM vertex factor.

CP1+U(1)lattice gauge theory in three dimensions: Phase structure, spins, gauge bosons, and instantons

In this paper we study a 3D lattice spin model of CP$^1$ Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of CP$^1$ bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) (O(4)) spin model with long-range and/or multi-spin interactions. It is also closely related to the recently proposed "Ginzburg-Landau" theory for quantum phase transitions of $s=1/2$ quantum spin systems on a 2D square lattice at zero temperature. We numerically study the phase structure of the model by calculating specific heat, spin correlations, instanton density, and gauge-boson mass. The model has two phases separated by a critical line of second-order phase transition; O(3) spin-ordered phase and spin-disordered phase. The spin-ordered phase is the Higgs phase of U(1) gauge dynamics, whereas the disordered phase is the confinement phase. We find a crossover in the confinement phase which separates dense and dilute regions of instantons. On the critical line, spin excitations are gapless, but the gauge-boson mass is {\it nonvanishing}. This indicates that a confinement phase is realized on the critical line. To confirm this point, we also study the noncompact version of the model. A possible realization of a deconfinement phase on the criticality is discussed for the CP$^N$+U(1) model with larger $N$.