Underlying Gauge Theory Research Articles

Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice

We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with Nf = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is gVPP = 7.8 ± 0.6, not far from gρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling {g}_{mathrm{VPP}}^{mathrm{KSRF}} = 9.4 ± 0.6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.

Towards the underlying gauge theory of the pure spinor superstring

Previous attempts to determine the worldsheet origin of the pure spinor for­malism were not completely successful, but introduced important concepts that seem to be connected to its fundamental structure, e.g., emergent supersymmetry and the role of reparametrization symmetry. In this work, a new proposal towards the underlying gauge theory of the pure spinor superstring is presented, based on an extension of Berkovits’ twistor-like constraint. The gauge algebra is analyzed in detail and worldsheet reparametrization is shown to be a redundant symmetry. The master action is built with a careful account of the intrinsic gauge symmetries associated with the pure spinor constraint and a consistent gauge fixing is performed. After a field redefinition, spacetime supersymmetry emerges and the resulting action describes the pure spinor superstring.

Light Scalars in Composite Higgs Models

A composite Higgs boson is likely to be accompanied by additional light states generated by the same dynamics. This expectation is substantiated when realising the composite Higgs mechanism by an underlying gauge theory. We review the dynamics of such objects, which may well be the first sign of compositeness at colliders. We also update our previous analysis of the bounds from LHC searches to the latest results, and discuss the projected reach of the High-Luminosity run.

Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach, I. Tractors

Tractors and Twistors bundles both provide natural conformally covariant calculi on $4D$-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom-up from prolongation of defining differential equations. We propose alternative top-down gauge theoretic constructions starting from the conformal Cartan bundle $\mathcal{P}$ and its vectorial $E$ and spinorial $\mathsf{E}$ associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows to exhibit tractors and twistors and their associated connections as gauge fields of a nonstandard kind as far as Weyl rescaling symmetry is concerned. By which we mean that they implement the gauge principle but are of a different geometric nature than the well known differential geometric objects usually underlying gauge theories. We provide the corresponding BRST treatment. The present paper deals with the case of tractors while a companion paper deals with twistors.

Conformal QED in two-dimensional topological insulators

It has been shown that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). Here, we provide a first-principle derivation of this HLL based on the gauge-theory approach. We start by considering massless Dirac fermions confined on the one-dimensional boundary of the topological insulator and interacting through a three-dimensional quantum dynamical electromagnetic field. Within these assumptions, through a dimensional-reduction procedure, we derive the effective 1 + 1-dimensional interacting fermionic theory and reveal its underlying gauge theory. In the low-energy regime, the gauge theory that describes the edge states is given by a conformal quantum electrodynamics (CQED), which can be mapped exactly into a HLL with a Luttinger parameter and a renormalized Fermi velocity that depend on the value of the fine-structure constant α.

Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors

Tractor and Twistor bundles provide natural conformally covariant calculi on 4D-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom–up through prolongation of defining differential equations. We propose alternative top–down gauge theoretic constructions, starting from the conformal Cartan bundle and its vectorial E and spinorial associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows tractors and twistors and their associated connections to exhibit as gauge fields of a non-standard kind as far as Weyl rescaling transformation is concerned. By non-standard we mean that they implement the gauge principle of physics, but are of a different geometric nature than the well-known differential geometric objects usually underlying gauge theories. We provide the corresponding BRST treatment. In a companion paper we dealt with tractors, in the present one we address the case of twistors.

Schwarzschild instanton in emergent gravity

In the bottom-up approach of emergent gravity, we attempt to find symplectic gauge fields emerging from Euclidean Schwarzschild instanton, which is studied as electromagnetism defined on the symplectic space [Formula: see text]. Geometrical engineering with the emergent metric sets up the Seiberg–Witten map between commutative and non-commutative gauge fields, preparing the ground for the evaluation of topological invariants in terms of the underlying gauge theory quantities.

Weyl gravity and Cartan geometry

We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned by two theories: the first one will be the associated Yang-Mills-like Lagrangian, while the second, inspired by~\cite{Wheeler2014}, will be a slightly more general one which will relax the conformal Cartan geometry. The corresponding gauge symmetry is treated within the BRST language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the `normal conformal Cartan connection'. Finally, we provide in a Lagrangian framework a justification of the identification, in dimension $4$, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in \cite{Korz-Lewand-2003}.

The framed Standard Model (I) — A physics case for framing the Yang–Mills theory?

Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: the standard Higgs scalar as the framon in the electroweak sector; a global [Formula: see text] symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale [Formula: see text]. From previous work, it is known already that a rotating mass matrix will lead automatically to: CKM mixing and neutrino oscillations, hierarchical masses for quarks and leptons, a solution to the strong-CP problem transforming the theta-angle into a Kobayashi–Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.

UV descriptions of composite Higgs models without elementary scalars

We consider four-dimensional UV descriptions of composite Higgs models without elementary scalars, in which four-fermion interactions are introduced to an underlying gauge theory like in the gauged NJL model. When the anomalous dimension of the fermion bilinear is large, these interactions drive the spontaneous global symmetry breaking in the model, with the Higgs identified as a Nambu-Goldstone boson. The UV descriptions support composite top partner operators, also with large anomalous dimensions, thereby providing an explicit realisation of the idea of partial compositeness. In particular, the composite SO(6)/SO(5) model can be described by an Sp gauge theory with four flavours of fermion, together with a vector-like pair of fermions transforming in the antisymmetric representation and charged under SU(3) colour. These fermions confine to produce both the Higgs and top partner bound states. Our methods can also be applied to different coset groups, suggesting that four-fermion operators can describe the underlying UV dynamics of other composite Higgs models.

Effective Polyakov line action from strong lattice couplings to the deconfinement transition

We calculate the effective Polyakov line action corresponding to SU(2) lattice gauge theory on a 16^3 X 4 lattice via the "relative weights" method. We consider a variety of lattice couplings, ranging from beta=1.2 in the strong-coupling domain, to beta=2.3 at the deconfinement transition, in order to study how the effective action evolves with beta. Comparison of Polyakov line correlators computed in the effective theory and the underlying gauge theory is used to test the validity of the effective action for beta > 1.4, while for beta=1.2, 1.4 we can compare our effective action to the one obtained from a low-order strong-coupling expansion. Very good agreement is found at all couplings. We find that the effective action is given by a simple expression bilinear in the Polyakov lines. The range of the bilinear term, away from strong coupling, grows rapidly in lattice units as beta increases.

Discovering Technicolor

We provide a pedagogical introduction to extensions of the Standard Model in which the Higgs is composite. These extensions are known as models of dynamical electroweak symmetry breaking or, in brief, Technicolor. Material covered includes: motivations for Technicolor, the construction of underlying gauge theories leading to minimal models of Technicolor, the comparison with electroweak precision data, the low-energy effective theory, the spectrum of the states common to most of the Technicolor models, the decays of the composite particles and the experimental signals at the Large Hadron Collider. The level of the presentation is aimed at readers familiar with the Standard Model but who have little or no prior exposure to Technicolor. Several extensions of the Standard Model featuring a composite Higgs can be reduced to the effective Lagrangian introduced in the text. We establish the relevant experimental benchmarks for Vanilla, Running, Walking, and Custodial Technicolor, and a natural fourth family of leptons, by laying out the framework to discover these models at the Large Hadron Collider.

Transverse structure of the QCD string

The characterization of the transverse structure of the QCD string is discussed. We formulate a conjecture as to how the stress-energy tensor of the underlying gauge theory couples to the string degrees of freedom. A consequence of the conjecture is that the energy density and the longitudinal-stress operators measure the distribution of the transverse position of the string, to leading order in the string fluctuations, whereas the transverse-stress operator does not. We interpret recent numerical measurements of the transverse size of the confining string and show that the difference of the energy and longitudinal-stress operators is a particularly natural probe at next-to-leading order. Second, we derive the constraints imposed by open-closed string duality on the transverse structure of the string. We show that a total of three independent ``gravitational'' form factors characterize the transverse profile of the closed string, and obtain the interpretation of recent effective string theory calculations: the square radius of a closed string of length $\ensuremath{\beta}$ defined from the slope of its gravitational form factor, is given by $\frac{d\ensuremath{-}1}{2\ensuremath{\pi}\ensuremath{\sigma}}\mathrm{log}\frac{\ensuremath{\beta}}{4{r}_{0}}$ in $d$ space dimensions. This is to be compared with the well-known result that the width of the open string at midpoint grows as $\frac{d\ensuremath{-}1}{2\ensuremath{\pi}\ensuremath{\sigma}}\mathrm{log}\frac{r}{{r}_{0}}$. We also obtain predictions for transition form factors among closed-string states.

Conformal chiral dynamics

We investigate the chiral dynamics of gauge theories developing an infrared stable fixed point. We determine the dependence of the bilinear fermion condensate on the underlying fermion mass and its anomalous dimension. We introduce the instanton contributions and investigate how they affect the dynamics near the fixed point. We generalize the Gell-Mann Oakes Renner relation and suggest to use it to uncover the presence of an infrared fixed point of the underlying gauge theory. Our results have an immediate impact on the construction of sensible extensions of the Standard Model of particle interactions and the general understanding of the phase diagram of strongly coupled theories.

Unitarity in technicolor

We investigate the longitudinal $WW$ scattering in models of dynamical electroweak symmetry breaking featuring a spin one axial and vector state and a composite Higgs. We also investigate the effects of a composite spin two state which has the same properties of a massive graviton. Any model of dynamical electroweak symmetry breaking will feature, depending on the dynamics, some or all these basic resonances as part of the low energy spectrum. We suggest how to take limits in the effective Lagrangian parameter space to reproduce the dynamics of different types of underlying gauge theories, from the traditional Technicolor models to the newest ones featuring nearly conformal dynamics. We study the direct effects of a light composite Higgs and the indirect ones stemming from the presence of a light axial resonance on the longitudinal $WW$ scattering.

Ultraminimal technicolor and its dark matter technicolor interacting massive particles

We introduce an explicit model with technifermion matter transforming according to multiple representations of the underlying technicolor gauge group. The model features simultaneously the smallest possible value of the naive $S$ parameter and the smallest possible number of technifermions. The chiral dynamics is extremely rich. We construct the low-energy effective Lagrangian. We provide both the linearly and nonlinearly realized ones. We then embed, in a natural way, the standard model (SM) interactions within the global symmetries of the underlying gauge theory. Several low-energy composite particles are SM singlets. One of these technicolor interacting massive particles (TIMP)s is a natural cold dark matter (DM) candidate. We estimate the fraction of the mass in the universe constituted by our DM candidate over the baryon one. We show that the new TIMP, differently from earlier models, can be sufficiently light to be directly produced and studied at the Large Hadron Collider (LHC).

Conformal windows of SU(N) gauge theories, higher dimensional representations, and the size of the unparticle world

We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vectorlike matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories developing an infrared stable fixed point. We find that exactly 50% of the asymptotically free theories can develop an infrared fixed point while for the nonsupersymmetric theories it is circa 25%. When considering multiple representations, only for the nonsupersymmetric case, the conformal regions quickly dominate over the nonconformal ones. For four representations, 70% of the asymptotically free space is filled by the conformal region. According to our theoretical landscape survey the unparticle physics world occupies a sizable amount of the particle world, at least in theory space, and before mixing it (at the operator level) with the nonconformal one.

Minimal walking technicolor: Setup for collider physics

Different theoretical and phenomenological aspects of the minimal and nonminimal walking technicolor theories have recently been studied. The goal here is to make the models ready for collider phenomenology. We do this by constructing the low energy effective theory containing scalars, pseudoscalars, vector mesons, and other fields predicted by the minimal walking theory. We construct their self-interactions and interactions with standard model fields. Using the Weinberg sum rules, opportunely modified to take into account the walking behavior of the underlying gauge theory, we find interesting relations for the spin-one spectrum. We derive the electroweak parameters using the newly constructed effective theory and compare the results with the underlying gauge theory. Our analysis is sufficiently general such that the resulting model can be used to represent a generic walking technicolor theory not at odds with precision data.

Topological entanglement entropy in the quantum dimer model on the triangular lattice

A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that in a topological phase there is a universal additive constant in the entanglement entropy, called the topological entanglement entropy, which reflects the underlying gauge theory for the topological order. In the present paper, we evaluate numerically the topological entanglement entropy in the ground-states of a quantum dimer model on the triangular lattice, which is known to have a dimer liquid phase with Z_2 topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for Z_2 topological order. We also consider the entanglement entropy on a topologically non-trivial ``zigzag'' area and propose to use it as another way to measure the topological entropy.

Light composite Higgs boson from higher representations versus electroweak precision measurements: Predictions for CERN LHC

We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide useful constraints on the relative mass splitting of the new leptons needed to cure the Witten anomaly. In the case of a fourth family of leptons with ordinary lepton hypercharge the new heavy neutrino can be a natural candidate of cold dark matter. We also propose theories in which the critical number of flavors needed to enter the conformal window is higher than the one with fermions in the two-index symmetric representation, but lower than in the walking technicolor theories with fermions only in the fundamental representation of the gauge group. Due to the near conformal/chiral phase transition, we show that the composite Higgs is very light compared to the intrinsic scale of the technicolor theory. For the two technicolor theory we predict the composite Higgs mass not to exceed 150 GeV.