Non-vanishing Vacuum Expectation Value Research Articles

Effective Potential for Conformal Factor and GL(4) Symmetry

Abstract We revisit the issue that the effective potential for the conformal factor of the metric, which is generated by
quantized matter fields, possesses a non-vanishing vacuum expectation value (VEV) or not. We prove that the effective
potential has a vanishing vacuum expectation value on the basis of a global $GL(4)$ symmetry. We also account for the
reason why there seem to be two different effective potentials for the conformal factor in a theory, one of which
gives rise to a vanishing VEV for the conformal factor whereas the other does a non-vanishing VEV. 

Scale invariance beyond criticality within the mean-field analysis of tensorial field theories

We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a Schrödinger equation. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

Gravitational waves from the high temperature electroweak symmetry nonrestoration

The high temperature electroweak symmetry nonrestoration (SNR) opens a window to realize baryogenesis at high energy scales, which can alleviate the tight phenomenological constraints. An effective way to realize the electroweak SNR is to extend the Standard Model (SM) by adding a second Higgs doublet and a few new singlet fermions which interact with the second Higgs through a five-dimension operator. In this scenario, the second Higgs has a nonvanishing vacuum expectation value above the electroweak scale and thus breaks the electroweak symmetry. As the temperature decreases, the SM electroweak phase transition occurs and the Universe is located at SM electroweak vacuum. We show that the electroweak phase transition is the first order and the gravitational waves (GWs) generated during this process can be detected by the future GW experiments such as LISA, TianQin, DECIGO, and BBO.

Pseudo-Nambu-Goldstone dark matter from non-Abelian gauge symmetry

We propose a pseudo-Nambu-Goldstone boson (pNGB) dark matter (DM) model based on an additional non-Abelian gauge symmetry $SU(2{)}_{D}$. The gauge symmetry $SU(2{)}_{D}$ is spontaneously broken to a global custodial symmetry $U(1{)}_{V}$ via the nonvanishing vacuum expectation values of $SU(2{)}_{D}$ doublet and triplet scalar fields. Due to the exact global symmetry $U(1{)}_{V}$, the lightest $U(1{)}_{V}$ charged particle becomes stable. We assume that the lightest charged particle in the model is the charged complex pNGB, which we regard as DM. It avoids the strong constraints from current DM direct detection experiments due to the property of NGB. We find that the measured energy density of DM can be reproduced when the DM mass is larger than the half of the Higgs mass, where the lower limit generally comes from the constraint of DM invisible decay and the upper limit from DM direct detection experiments depends on the model parameters.

Thraxions: towards full string models

We elucidate various aspects of the physics of thraxions, ultra-light axions arising at Klebanov-Strassler multi-throats in the compactification space of IIB superstring theory. We study the combined stabilization of Kähler moduli and thraxions, showing that under reasonable assumptions, one can solve the combined problem both in a KKLT and a LVS setup. We find that for non-minimal multi-throats, the thraxion mass squared is three-times suppressed by the throat warp factor. However, the minimal case of a double-throat can preserve the six-times suppression as originally found. We also discuss the backreaction of a non-vanishing thraxion vacuum expectation value on the geometry, showing that it induces a breaking of the imaginary self-duality condition for 3-form fluxes. This in turn breaks the Calabi-Yau structure to a complex manifold one. Finally, we extensively search for global models which can accommodate the presence of multiple thraxions within the database of Complete Intersection Calabi-Yau orientifolds. We find that each multi-throat system holds a single thraxion. We further point out difficulties in constructing a full-fledged global model, due to the generic presence of frozen-conifold singularities in a Calabi-Yau orientifold. For this reason, we propose a new database of CICY orientifolds that do not have frozen conifolds but that admit thraxions.

Thermodynamics of a Two-Step Electroweak Phase Transition.

New field content beyond that of the standard model of particle physics can alter the thermal history of electroweak symmetry breaking in the early Universe. In particular, the symmetry breaking may have occurred through a sequence of successive phase transitions. We study the thermodynamics of such a scenario in a real triplet extension of the standard model, using nonperturbative lattice simulations. Two-step electroweak phase transition is found to occur in a narrow region of allowed parameter space with the second transition always being first order. The first transition into the phase of nonvanishing triplet vacuum expectation value is first order in a non-negligible portion of the two-step parameter space. A comparison with two-loop perturbative calculation is provided and significant discrepancies with the nonperturbative results are identified.

Emergent symmetries of the Standard Model

We show how, using multipartite entanglement, the symmetries among bosons and fermions of the Standard Model of particle physics emerge. Fermions belong to tripartite maximally entangled classes starting with basic chiral right and left states. Quarks and leptons belong to different classes, with only leptons appearing as asymptotic states in three space dimensions. The Higgs boson is the scalar mode with a nonvanishing vacuum expectation value, other bosons are as usual linked to symmetry generators.

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.

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.

Exact Holography of Massive M2-brane Theories and Entanglement Entropy

We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with Uk(N) × U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤk × SO(4)=ℤk isometry. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein (KK) holography to the LLM geometries. We focus on the chiral primary operator (CPO) with conformal dimension Δ = 1. The non-vanishing vacuum expectation value (vev) implies the breaking of conformal symmetry. In that case, we show that the variation of the holographic entanglement entropy (HEE) from it’s value in the CFT, is related to the non-vanishing one-point function due to the relevant deformation as well as the source field. Applying Ryu Takayanagi’s HEE conjecture to the 4-dimensional gravity solutions, which are obtained from the KK reduction of the 11-dimensional LLM solutions, we calculate the variation of the HEE. We show how the vev and the value of the source field determine the HEE.

Gauge-independent Higgs mechanism and the implications for quark confinement

We propose a gauge-invariant description for the Higgs mechanism by which a gauge boson acquires the mass. We do not need to assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. For concreteness, we discuss the gauge-Higgs models with $U(1)$ and $SU(2)$ gauge groups explicitly. This enables us to discuss the confinement-Higgs complementarity from a new perspective.

Gauge-invariant description of Higgs phenomenon and quark confinement

We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant Higgs phenomenon for the relevant Yang-Mills-Higgs model.

Charge and color breaking constraints in the Minimal Supersymmetric Standard Model associated with the bottom Yukawa coupling

Testing the stability of the electroweak vacuum in any extension of the Standard Model Higgs sector is of great importance to verify the consistency of the theory. Multi-scalar extensions as the Minimal Supersymmetric Standard Model generically lead to unstable configurations in certain regions of parameter space. An exact minimization of the scalar potential is rather an impossible analytic task. To give handy analytic constraints, a specific direction in field space has to be considered which is a simplification that tends to miss excluded regions, however good to quickly check parameter points. We describe a yet undescribed class of charge and color breaking minima as they appear in the Minimal Supersymmetric Standard Model, exemplarily for the case of non-vanishing bottom squark vacuum expectation values constraining the combination μYb in a non-trivial way. Contrary to famous A-parameter bounds, we relate the bottom Yukawa coupling with the supersymmetry breaking masses. Another bound can be found relating soft breaking masses and μ only. The exclusions follow from the tree-level minimization and can change dramatically using the one-loop potential. Estimates of the lifetime of unstable configurations show that they are either extremely short- or long-lived.

The Abelian Higgs model and a minimal length in an un-particle scenario

We consider both the Abelian Higgs model and the impact of a minimal length in the un-particle sector. It is shown that even if the Higgs field takes a non-vanishing vacuum expectation value (v.e.v.), gauge interaction keeps its long-range character leading to an effective gauge symmetry restoration. The effect of a quantum-gravity–induced minimal length on a physical observable is then estimated by using a physically based alternative to the usual Wilson loop approach. Interestingly, we obtain an ultraviolet finite interaction energy described by a confluent hypergeometric function, which shows a remarkable richness of behavior.

Color breaking in the early universe

We explore the possibility that $\mathrm{SU}(3{)}_{C}$ was not an exact symmetry at all times in the early Universe, using minimal extensions of the standard model that contain a color triplet scalar field and perhaps other fields. We show that, for a range of temperatures, there can exist a phase in which the free energy is minimized when the color triplet scalar has a nonvanishing vacuum expectation value, spontaneously breaking color. At very high temperatures and at lower temperatures, color symmetry is restored. The breaking of color in this phase is accompanied by the spontaneous breaking of $B\ensuremath{-}L$ if the color triplet scalar Yukawa couples to quarks and/or leptons. We discuss the requirements on the minimal extensions needed for consistency of this scenario with present collider bounds on new colored scalar particles.

Chiral phase transition in a planar four-Fermi model in a tilted magnetic field

We study a planar four-Fermi Gross-Neveu model in the presence of a tilted magnetic field, with components parallel and perpendicular to the system's plane. We determine how this combination of magnetic field components, when applied simultaneously, affects the phase diagram of the model. It is shown that each component of the magnetic field causes a competing effect on the chiral symmetry in these fermionic systems. While the perpendicular component of the magnetic field tends to make the chiral symmetry breaking stronger, the effect of the parallel component of the field in these planar systems is to weaken the chiral symmetry through the enhancement of the Zeeman energy term. We show that this competing effect, when combined also with temperature and chemical potential, can lead to a rich phase diagram, with the emergence of multiple critical points and reentrant phase transitions. We also study how the presence of these multiple critical points and reentrant phases can manifest in the quantum Hall effect. Our results provide a possible way to probe experimentally chiral symmetry breaking and the corresponding emergence of a gap (i.e., the presence of a nonvanishing chiral vacuum expectation value) in planar condensed matter systems of current interest.

Decoupling limits in multi-sector supergravities

Conventional approaches to cosmology in supergravity assume the existence of multiplesectors that only communicate gravitationally.In principle thesesectors decouple in the limit Mpl→∞. Inpractice such a limit is delicate: for generic supergravities,where sectors are combined by adding their Kähler functions, theseparate superpotentials must contain non-vanishing vacuumexpectation values supplementing the naïve global superpotential. We show that thisrequires non-canonical scaling in the naïve supergravitysuperpotential couplings to recover independent sectors ofglobally supersymmetric field theory in the decoupling limit Mpl → ∞.

Superpotential de-sequestering in string models

Non-perturbative superpotential cross-couplings between visible sector matter and K\"ahler moduli can lead to significant flavour-changing neutral currents in compactifications of type IIB string theory. Here, we compute corrections to Yukawa couplings in orbifold models with chiral matter localised on D3-branes and non-perturbative effects on distant D7-branes. By evaluating a threshold correction to the D7-brane gauge coupling, we determine conditions under which the non-perturbative corrections to the Yukawa couplings appear. The flavour structure of the induced Yukawa coupling generically fails to be aligned with the tree-flavour structure. We check our results by also evaluating a correlation function of two D7-brane gauginos and a D3-brane Yukawa coupling. Finally, by calculating a string amplitude between n hidden scalars and visible matter we show how non-vanishing vacuum expectation values of distant D7-brane scalars, if present, may correct visible Yukawa couplings with a flavour structure that differs from the tree-level flavour structure.

Can supersymmetry breaking lead to electroweak symmetry breaking via formation of scalar bound states?

The recent discovery of the putative 125 GeV Higgs boson has motivated a number of attempts to reconcile its relatively large mass with the predictions of the minimal supersymmetric standard model (MSSM). Some approaches invoked large trilinear supersymmetry breaking terms At between stops and one of the elementary Higgs fields. We consider the possibility that electroweak symmetry breaking may be triggered by supersymmetry breaking with a large At, large enough to generate a composite field with the same quantum numbers as the Higgs boson and with a non-vanishing vacuum expectation value. In the resulting vacuum, the usual relation between the gauge couplings and the Higgs self-coupling does not apply, and there is no reason to expect the same upper bound on the mass of the lightest Higgs boson. In a simple model where the bound state is assumed to have no mixing with the other fields, we calculate the critical coupling At necessary for symmetry breaking using the lowest-order Bethe–Salpeter (BS) equation. Study of the BS equation is complicated by the structure of its lowest-order kernel, which is a crossed box graph, but we find an accurate approximation to its solution. In a realistic model, the mixing of the bound state with the fundamental Higgs boson creates a symmetry-breaking seesaw. We outline the steps toward a realistic model.