Adjoint Scalar Field Research Articles

Gauge-independent transition dividing the confinement phase in the lattice SU(2) gauge-adjoint scalar model

The lattice SU(2) gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations that have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism. In this paper, we reexamine this phase structure in a gauge-independent way based on the numerical simulations performed without any gauge fixing. This is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanism for generating the mass of the gauge field without relying on any spontaneous symmetry breaking. For this purpose, we investigate correlations between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field which is constructed from the gauge field based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. Consequently, we reproduce gauge independently the transition line separating the confinement phase and the Higgs phase, and show surprisingly the existence of a new transition line that completely divides the confinement phase into two parts. Finally, we discuss the physical meaning of the new transition and the implications of the confinement mechanism. Published by the American Physical Society 2024

The loom for general fishnet CFTs

We propose a broad class of d-dimensional conformal field theories of SU(N) adjoint scalar fields generalising the 4d Fishnet CFT (FCFT) discovered by Ö. Gürdogan and one of the authors as a special limit of γ-deformed mathcal{N} = 4 SYM theory. In the planar N → ∞ limit the FCFTs are dominated by the “fishnet” planar Feynman graphs. These graphs are explicitly integrable, as was shown long ago by A. Zamolodchikov. The Zamolodchikov’s construction, based on the dual Baxter lattice (straight lines on the plane intersecting at arbitrary slopes) and the star-triangle identities, can serve as a “loom” for “weaving” the Feynman graphs of these FCFTs, with certain types of propagators, at any d. The Baxter lattice with M different slopes and any number of lines parallel to those, generates an FCFT consisting of M (M – 1) fields and a certain number of chiral vertices of different valences with distinguished couplings. These non-unitary, logarithmic CFTs enjoy certain reality properties for their spectrum due to a symmetry similar to the PT-invariance of non-hermitian hamiltonians proposed by C. Bender and S. Boettcher. We discuss in more detail the theories generated by a loom with M = 2, 3, 4, and the generalisation of the loom FCFTs for spinning fields in 4d.

Construction of non-Abelian electric strings

We detail the construction of electric string solutions in $SU(2)$ Yang-Mills-Higgs theory with a scalar in the fundamental representation and discuss the properties of the solution. We show that Schwinger gluon pair production in the electric string background is absent. A similar construction in other models, such as with an adjoint scalar field and the electroweak model, does not yield solutions.

Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition

We study the crossover phase transition of the SU(2) Georgi-Glashow model in three dimensions. In this model, a confining condensate of topological ’t Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo simulations to study the monopole gas across a crossover transition, and demonstrate that gradient flow can be used to renormalize the otherwise divergent monopole number density. The condensation of the monopoles means that the theory admits also a massive photon-like excitation. We show that the renormalized monopole number density is approximately proportional to the square of the photon mass, in agreement with semiclassical results. Our results give insight into behaviour of the Higgs regime near crossover, which has boarder implications for beyond the Standard Model theories containing adjoint scalar fields.

Radiative interactions between new non-Abelian gauge sector and the standard model

We discuss one loop generation of the term connecting gauge fields from a local hidden SU(2)H and the standard model U(1)Y introducing an SU(2)H doublet fermion with non-zero hypercharge and a scalar field in adjoint representation. Then we obtain a kinetic mixing term between SU(2)H and U(1)Y gauge fields after the adjoint scalar field developing vacuum expectation value. We illustrate such a concrete scenario introducing a dark matter model in an ultraviolet (UV) completion with local SU(2)H symmetry where the scalar doublet is our dark matter candidate and its stability is guaranteed by remnant Z2 symmetry from SU(2)H. Relic density of dark matter is calculated focusing on the case in which dark matter annihilate into known particles via SU(2)H gauge interactions with radiatively induced kinetic mixing.

BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric Yang-Mills-Higgs models

We investigate an effective flavor-symmetric Yang-Mills-Higgs model with $N^2-1$ adjoint scalar fields. We find a set of BPS equations that provide vortex solutions and calculate their energies for arbitrary representations. We show that, for a given N-ality $k$, the energy of the corresponding antisymmetric representation is the lowest. This completes the proof that this model is able to reproduce a Casimir law for the string tension at asymptotic distances.

Dyon in the SU(2) Yang\u2013Mills theory with a gauge-invariant gluon mass toward quark confinement

In the previous paper, we have shown the existence of magnetic monopoles in the pure SU(2) Yang–Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the SU(2) “complementary” gauge-scalar model, which is the SU(2) Yang–Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang–Mills theory. Moreover, we compare the dyon of the massive Yang–Mills theory obtained in this way with the Julia–Zee dyon in the Georgi–Glashow gauge-Higgs scalar model and the dyonic extension of the Wu–Yang magnetic monopole in the pure Yang–Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on S^1 times {mathbb {R}}^3 space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang–Mills theory at finite temperature, instead of using the dyons constituting the Kraan–van Baal–Lee–Lu caloron.

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory.

We show that N=4 supersymmetric-Yang-Mills (SYM) theory on R×S^{3} with gauge group SU(N) is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with SU(1,1)×U(1) invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the SU(1,1) sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a (1+1)-dimensional complex chiral boson on a circle coupled to a nondynamical gauge field, both in the adjoint representation of SU(N). The successful construction of a lower-dimensional nonrelativistic field theory in the SU(1,1) near-BPS limit provides a proof of concept for other BPS bounds. These are expected to lead to richer field theories in nonrelativistic corners of N=4 SYM that include fermions, gauge fields, and supersymmetry and can provide a novel path towards understanding strongly coupled finite-N dynamics of gauge theories.

Deconfined criticality in the QED3 Gross-Neveu-Yukawa model: The 1/N expansion revisited

The critical properties of the QED$_{3}$ Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the N\'eel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $\epsilon$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED$_{3}$ GNY critical point are in reasonable agreement with numerical studies of the N\'eel-to-VBS transition, in support of the duality conjecture.

Magnetic monopoles in pure $SU (2)$ Yang–Mills theory with a gauge-invariant mass

In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining the gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model with the radial length of the scalar field being fixed. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism which neither relies on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. According to these procedures, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ Yang-Mills theory coupled with an adjoint scalar field whose radial degree of freedom is fixed, and obtain a gauge field configuration of magnetic monopole with a minimum magnetic charge in the massive $SU(2)$ Yang-Mills theory. We compare the magnetic monopole obtained in this way in the massive Yang--Mills theory with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow model.

Skyrme–Faddeev model from 5d super-Yang–Mills

We consider 5d Yang–Mills–Higgs theory with a compact ADE-type gauge group G and one adjoint scalar field on R3,1×R+, where R+=[0,∞) is the half-line. The maximally supersymmetric extension of this model, with five adjoint scalars, appears after a reduction of 6d N=(2,0) superconformal field theory on R3,1×R+×S1 along the circle S1. We show that in the low-energy limit, when momenta along R3,1 are much smaller than along R+, the 5d Yang–Mills–Higgs theory reduces to a nonlinear sigma model on R3,1 with a coset G/H as its target space. Here H is a closed subgroup of G determined by the Higgs-field asymptotics at infinity. The 4d sigma model describes an infinite tower of interacting fields, and in the infrared it is dominated by the standard two-derivative kinetic term and the four-derivative Skyrme–Faddeev term.

Inflation from a no-scale supersymmetric SU(4)C×SU(2)L×SU(2)R model

We study inflation in a supersymmetric Pati-Salam model driven by a potential generated in the context of no-scale supergravity. The Pati-Salam gauge group $SU(4)_{c}\times{SU(2)_{L}\times{SU(2)_{R}}}$ , is supplemented with a $Z_{2} $ symmetry. Spontaneous breaking via the $SU(4)$ adjoint leads to the left-right symmetric group. Then the $SU(2)_{R}$ breaks at an intermediate scale and the inflaton is a combination of the neutral components of the $SU(2)_{R}$ doublets. We discuss various limits of the parameter space and we show that consistent solutions with the cosmological data for the a spectral index $n_{s}$ and the tensor-to-scalar ratio r are found for a wide range of the parameter space of the model. Regarding the latter, which is a canonical measure of primordial gravity waves, we find that $r\sim{10^{-3}-10^{-2}}$. An alternative possibility where the adjoint scalar field $S$ has the role of the inflaton is also discussed.

Gauge-independent Brout\u2013Englert\u2013Higgs mechanism and Yang\u2013Mills theory with a gauge-invariant gluon mass term

For the Yang–Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout–Englert–Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang–Mills theory with an adjoint scalar field. Moreover, we show that the Yang–Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin–Shenker continuity and Osterwalder–Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout–Englert–Higgs mechanism by starting with the complementary gauge-scalar model.

Emergent Yang–Mills theories from universal extra dimensions

We study emergent Yang–Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang–Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.

Gauge symmetries emerging from extra dimensions

We argue that extra dimensions with a properly chosen compactification scheme could be a natural source for emergent gauge symmetries. Actually, some proposed vector field potential terms or polynomial vector field constraints introduced in five-dimensional Abelian and non-Abelian gauge theory is shown to smoothly lead to spontaneous violation of an underlying 5D spacetime symmetry and generate pseudo-Goldstone vector modes as conventional 4D gauge boson candidates. As a special signature, there appear, apart from conventional gauge couplings, some properly suppressed direct multi-photon (multi-boson, in general) interactions in emergent QED and Yang-Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in emergent Yang-Mills theories an internal symmetry G also occurs spontaneously broken to its diagonal subgroups once 5D Lorentz violation happens. This breaking origins from the extra vector field components playing a role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when being applied to Grand Unified Theories this results in a fact that the emergent GUTs generically appear broken down to the Standard Model just at the 5D Lorentz violation scale M. PACS numbers: 11.15.-q, 11.30.Cp, 11.30.Pb, 11.10.Kk

SU(2) Yang–Mills Theory: Waves, Particles, and Quantum Thermodynamics

We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical S U ( 2 ) Yang–Mills theory on a four-dimensional Euclidean spacetime slice S 1 × R 3 . The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electric-magnetically (anti)selfdual in a non-trivial way and possess topological charge modulus unity. Their trivial-holonomy versions—Harrington–Shepard (HS) (anti)calorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarse-grained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field ϕ ( | ϕ | spatio-temporally constant). The field ϕ , in turn, implies an effective pure-gauge configuration, a μ gs , accurately describing HS (anti)caloron overlap. Spatial homogeneity of the thermal ground-state estimate ϕ , a μ gs demands that (anti)caloron centers are densely packed, thus representing a collective departure from (anti)selfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite ground-state energy density ρ gs and pressure P gs with ρ gs = − P gs as well as the (adjoint) Higgs mechanism. The peripheries of HS (anti)calorons are static and resemble (anti)selfdual dipole fields whose apparent dipole moments are determined by | ϕ | and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anti)caloron centers. Thus the vacuum electric permittivity ϵ 0 and magnetic permeability μ 0 , supporting the propagation of wave-like disturbances in the U ( 1 ) Cartan subalgebra of S U ( 2 ) , can be reliably calculated for disturbances which do not probe HS (anti)caloron centers. Both ϵ 0 and μ 0 turn out to be temperature independent in thermal equilibrium but also for an isolated, monochromatic U ( 1 ) wave. HS (anti)caloron centers, on the other hand, react onto wave-like disturbances, which would resolve their spatio-temporal structure, by indeterministic emissions of quanta of energy and momentum. Thermodynamically seen, such events are Boltzmann weighted and occur independently at distinct locations in space and instants in (Minkowskian) time, entailing the Bose–Einstein distribution. Small correlative ramifications associate with effective radiative corrections, e.g., in terms of polarization tensors. We comment on an S U ( 2 ) × S U ( 2 ) based gauge-theory model, describing wave- and particle-like aspects of electromagnetic disturbances within the so far experimentally/observationally investigated spectrum.

Solitons on intersecting 3-branes

We consider a system consisting of a pair of D3 branes intersecting each other along a line such that half of the 16 supersymmetries are preserved. We then study the existence of magnetic monopole solutions corresponding to a D1-brane suspended between these D3 branes. We consider this problem in the zero slope limit where the tilt of the D3-branes is encoded in the uniform gradient of the adjoint scalar field. Such a system is closely related to the non-abelian flux background considered originally by van Baal. We provide three arguments supporting the existence of a single magnetic monopole solution. We also comment on the relation between our construction and a recent work by Mintun, Polchinski, and Sun.

Giant monopoles as a dark matter candidate

The most prominent successes of weakly interacting massive particle (WIMP) models of dark matter are at comoving scales of megaparsecs. At kiloparsec scales they face challenges in explaining the density profiles, abundances and phase space distributions of satellite galaxies in our local group. An alternate dark matter candidate, the giant 't Hooft-Polyakov monopole, is proposed which may share the large distance successes of WIMPs while evading their short distance problems. These are classical field theory solutions of a dark sector including a nonabelian gauge field, an adjoint scalar field and fundamental fermions. In such models each halo consists of a single monopole characterized by a conserved integer charge.

HIGH Q BPS MONOPOLE BAGS ARE URCHINS

It has been known for 30 years that 't Hooft–Polyakov monopoles of charge Q greater than one cannot be spherically symmetric. Five years ago, Bolognesi conjectured that, at some point in their moduli space, BPS monopoles can become approximately spherically symmetric in the high Q limit. In this paper, we determine the sense in which this conjecture is correct. We consider an SU(2) gauge theory with an adjoint scalar field, and numerically find configurations with Q units of magnetic charge and a mass which is roughly linear in Q, for example, in the case Q = 81 we present a configuration whose energy exceeds the BPS bound by about 54%. These approximate solutions are constructed by gluing together Q cones, each of which contains a single unit of magnetic charge. In each cone, the energy is largest in the core, and so a constant energy density surface contains Q peaks and thus resembles a sea urchin.

Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies

A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $\phi$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in confining phases of SU(2) Yang-Mills theories neutrino mass $m_\nu$ solely arises by interactions with an environment. Cosmologically, the CMB represents this environment, and thus one would expect that $m_\nu=\xi T$ where $\xi=O(1)$. In this model cosmic neutrinos are a small dark-matter contribution, conserved only together with the CMB fluid, influencing Baryonic Acoustic Oscillations during CMB decoupling.