Massive Kaluza-Klein Research Articles

Weakly constrained double field theory as the double copy of Yang-Mills theory

The weakly constrained double field theory, in the sense of Hull and Zwiebach, captures the subsector of string theory on toroidal backgrounds that includes gravity, B-field, and dilaton together with all of their massive Kaluza-Klein and winding modes, which are encoded in doubled coordinates subject to the “weak constraint.” Due to the complications of the weak constraint, this theory was only known to cubic order. Here we construct the quartic interactions for the case that all dimensions are toroidal and doubled. Starting from the kinematic C∞ algebra K of pure Yang-Mills theory and its hidden Lie-type algebra, we construct the L∞ algebra of weakly constrained double field theory on a subspace of the “double copied” tensor product space K⊗K¯, by doing homotopy transfer to the weakly constrained subspace and performing a nonlocal shift that is well-defined on the torus. We test the resulting three-brackets and establish their uniqueness up to cohomologically trivial terms, by verifying the Jacobi identities up to homotopy for the gauge sector. Published by the American Physical Society 2024

Bounds on tower mass scales in the presence of throats of different warping

In Type IIB flux compactification realizing the metastable de Sitter (dS) vacuum, the uplift potential can be generated by D3‾-branes at the tip of Klebanov-Strassler throat. Then the uplift potential obeys the scaling law with respect to the tower mass scale msc, which can be the Kaluza-Klein (KK) mass scale associated with the throat containing D3‾-branes or the bulk tower mass scales, depending on the warping of the throat. On the other hand, in the presence of another throat of stronger warping, the KK mass scale associated with this throat is lower than msc. Nevertheless, the Higuchi bound and the condition that the tower mass scale is higher than the gravitino mass provide the upper bound on msc determined by the lowest tower mass scale (or gravitino mass). This bound also can be interpreted as the lower bound on the lowest tower mass scale determined by msc. We investigate this bound in detail when the throat containing D3‾-branes is strongly and weakly warped, respectively.

On the cosmological constant, the KK mass scale, and the cut-off dependence in the dark dimension scenario

In this short note we comment on the relation between the cosmological and the Kaluza–Klein mass scale in the dark dimension scenario [1], also in view of some recent claims [2] that would raise some doubts about the validity of this scenario. Here we argue that these claims have serious flaws and cannot be trusted.

Localization of gravitino field with non-minimal coupling on a thick brane

In this paper, we investigate localization of a five-dimensional gravitino field on a thick brane with non-minimal coupling. By choosing the gauge condition Ψ z = 0, the equations of the Kaluza-Klein (KK) modes of gravitino are obtained. Compared with the case without non-minimal coupling,considering non-minimal coupling can make the zero mode and massive KK modes of a five-dimensional free massless gravitino field be localized on the brane. By considering the Yukawa-like coupling and the non-minimum coupling simultaneously, it is found that the non-minimal coupling will change the mass spectrum of the KK modes and provide more possibility to localize KK modes.

Black holes and nilmanifolds: quasinormal modes as the fingerprints of extra dimensions?

We investigate whether quasinormal modes (QNMs) can be used in the search for signatures of extra dimensions. To address a gap in the Beyond the Standard Model (BSM) literature, we focus here on higher dimensions characterised by negative Ricci curvature. As a first step, we consider a product space comprised of a four-dimensional Schwarzschild black hole space-time and a three-dimensional nilmanifold (twisted torus); we model the black hole perturbations as a scalar test field. We suggest that the extra-dimensional geometry can be stylised in the QNM effective potential as a squared mass-like term representing the Kaluza–Klein (KK) spectrum. We then compute the corresponding QNM spectrum using three different numerical methods, and determine a possible “detectability bound” beyond which KK masses cannot be detected using QNMs.

Massive color-kinematics duality and double-copy for Kaluza-Klein scattering amplitudes

We study the structure of scattering amplitudes of massive Kaluza-Klein (KK) states under toroidal compactification. We present a shifting method to quantitatively derive the scattering amplitudes of massive KK gauge bosons and KK gravitons from the corresponding massless amplitudes in the noncompactified higher dimensional theories. With these we construct the massive KK scattering amplitudes by extending the double-copy relations of massless scattering amplitudes within the field theory framework, including both the BCJ and CHY methods, and build up their connections to the massive KK KLT relations. We present the massive BCJ-type double-copy construction of the N-point KK gauge boson/graviton scattering amplitudes, and as the applications we derive explicitly the four-point KK scattering amplitudes as well as the five-point KK scattering amplitudes. We further study the nonrelativistic limit of these massive scattering amplitudes with the heavy external KK states and discuss the impact of the compactified extra dimensions on the low energy gravitational potential. Finally, we analyze the four-point and N-point mass spectral conditions and newly propose a novel group theory approach to prove that only the KK theories under toroidal compactification can satisfy these conditions for directly realizing massive double-copy in the field theory framework.

Cylinder quantum field theories at small coupling

We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential V is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential V and an infinite tower of free massive Kaluza-Klein (KK) modes. Moving slightly away from the deep IR region has the effect of switching on interactions between the zero mode and the KK modes, whose strength is controlled by powers of the coupling, hence making the interactions increasingly suppressed. We take the notable example of Liouville field theory and, starting from its worldline version, we compute the torus (one-loop) partition function perturbatively in the coupling constant. The partition function at leading order is invariant under a T-duality transformation that maps the radius of the cylinder to its inverse and rescales it by the square of the Schwinger parameter of the cylinder. We show that this behavior is a universal feature of cylinder QFTs.

Structure of Kaluza-Klein graviton scattering amplitudes from the gravitational equivalence theorem and double copy

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_\xi$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

Signals of W′ and Z′ bosons at the LHC in the SU(3)×SO(5)×U(1) gauge-Higgs unification

The $pp\to \{W, W'\} \to l\nu$ and $pp\to \{\gamma, Z, Z'\} \to l^+l^-$ ($l=e,\mu$) processes in the $SU(3)_C\times SO(5)\times U(1)_X$ gauge-Higgs unification (GHU) models are studied, where $W'$ and $Z'$ bosons are Kaluza-Klein (KK) exited states of the electroweak gauge bosons. From the experimental data collected at the Large Hadron Collider, constraints on the KK mass scale and the Aharonov-Bohm phase are obtained. One can explore the KK mass scale in the GUT inspired GHU model up to 18 TeV for the luminosity 300 fb$^{-1}$ and 22 TeV for the luminosity 3000 fb$^{-1}$ at $\sqrt{s}=14$ TeV.

Addendum to “Leptophilic U(1) massive vector bosons from large extra dimensions: Reexamination of constraints from LEP data” [Phys. Lett. B 820 (2021) 136585

Very recently, we proposed an explanation of the discrepancy between the measured anomalous magnetic moment of the muon and the Standard Model (SM) prediction in which the dominant contribution to (g−2)μ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. In this addendum we reexamine the bounds on 4-fermion contact interactions from precise electroweak measurements and show that the constraints on KK masses and couplings are more severe than earlier thought. However, we demonstrate that our explanation remains plausible if a few KK modes are lighter than LEP energy, because if this were the case the contribution to the 4-fermion scattering from the internal propagator would be dominated by the energy and not by the mass. To accommodate the (g−2)μ discrepancy we assume that the lepton number L does not partake in the hypercharge and propagates in one extra dimension (transverse to the SM branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP energy), the string scale is roughly 10 TeV while the L gauge coupling is of order ∼10−1.

Ultraviolet sensitivity of Casimir energy

Abstract We quantitatively estimate the effect of ultraviolet (UV) physics on the Casimir energy in a five-dimensional (5D) model on S1/Z2. If the cutoff scale of the 5D theory is not far from the compactification scale, the UV physics may affect the low-energy result. We work in the cutoff regularization scheme by introducing two independent cutoff scales for the spatial momentum in the non-compact space and for the Kaluza–Klein masses. The effects of the UV physics are incorporated as a damping effect of the contributions to the vacuum energy around the cutoff scales. We numerically calculate the Casimir energy and evaluate the deviation from the result obtained in the zeta-function regularization, which does not include information on the UV physics. We find that the result agrees well with the latter for Gaussian-type damping, while it can deviate for kink-type damping.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on ${S}^{2}$ with monopolelike fluxes and also on ${\mathbb{CP}}^{2}$ with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Scattering amplitudes of Kaluza-Klein strings and extended massive double-copy

We study the scattering amplitudes of massive Kaluza-Klein (KK) states of open and closed bosonic strings under toroidal compactification. We analyze the structure of vertex operators for the KK strings and derive an extended massive KLT-like relation which connects the N-point KK closed-string amplitude to the products of two KK open-string amplitudes at tree level. Taking the low energy field-theory limit of vanishing Regge slope, we derive double-copy construction formula of the N-point massive KK graviton amplitude from the sum of proper products of the corresponding KK gauge boson amplitudes. Then, using the string-based massive double-copy formula, we derive the exact tree-level four-point KK gauge boson amplitudes and KK graviton amplitudes, which fully agree with those given by the KK field-theory calculations. With these, we give an explicit prescription on constructing the exact four-point KK graviton amplitudes from the sum of proper products of the corresponding color-ordered KK gauge boson amplitudes. We further analyze the string-based double-copy construction of five-point and six-point scattering amplitudes of massive KK gauge bosons and KK gravitons.

One-loop gluon amplitudes in AdS

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form AdSd+1× S3. For concreteness, we compute the one-loop correction to the massless gluon amplitude on AdS5×S3, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d mathcal{N} = 2 SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.

Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes

We analyze the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the KK gravitational Goldstone bosons in the compactified 5d general relativity (GR). Using a general R ξ gauge fixing, we study the geometric Higgs mechanism for the massive spin-2 KK gravitons. We newly propose and prove a gravitational equivalence theorem (GRET) to connect the scattering amplitudes of longitudinal KK gravitons to that of the KK gravitational Goldstone bosons, which formulates the geometric gravitational Higgs mechanism at the scattering S - matrix level. We demonstrate that the GRET provides a general energy cancellation mechanism guaranteeing the N -point longitudinal KK graviton scattering amplitudes to have their leading energy dependence cancelled down by a large power factor of E 2 N N ≥ 4 up to any loop level. We propose an improved double-copy approach to construct the massive KK graviton (Goldstone) amplitudes from the KK gauge boson (Goldstone) amplitudes. With these, we establish a new correspondence between the two types of energy cancellations in the four-point longitudinal KK amplitudes at tree level: E 4 ⟶ E 0 in the KK gauge theory and E 10 ⟶ E 2 in the KK GR theory.

Electroweak and left-right phase transitions in SO(5)×U(1)×SU(3) gauge-Higgs unification

The electroweak phase transition in GUT inspired $SO(5)\times U(1) \times SU(3)$ gauge-Higgs unification is shown to be weakly first order and occurs at $T = T_c^{\rm EW} \sim 163\,$GeV, which is very similar to the behavior in the standard model in perturbation theory. A new phase appears at higher temperatures. $SU(2)_L \times U(1)_Y$ ($\theta_H=0$) and $SU(2)_R \times U(1)_{Y'}$ ($\theta_H=\pi$) phases become almost degenerate above $T \sim m_{\rm KK}$ where $m_{\rm KK}$ is the Kaluza-Klein mass scale typically around 13$\,$TeV and $\theta_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T = T_c^{\rm LR} \sim m_{\rm KK}$. As the temperature drops in the evolution of the early Universe the $SU(2)_R \times U(1)_{Y'}$ phase becomes unstable. The tunneling rate from the $SU(2)_R \times U(1)_{Y'}$ phase to the $SU(2)_L \times U(1)_Y$ phase becomes sizable and a first-order phase transition takes place at $T=2.5 \sim 2.6\,$TeV. The amount of gravitational waves produced in this left-right phase transition is small, far below the reach of the sensitivity of Laser Interferometer Space Antenna (LISA). A detailed analysis of the $SU(2)_R \times U(1)_{Y'}$ phase is also given. It is shown that the $W$ boson, $Z$ boson and photon, with $\theta_H$ varying from 0 to $\pi$, are transformed to gauge bosons in the $SU(2)_R \times U(1)_{Y'}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2)_R \times U(1)_{Y'}$ phase are determined.

Codimension- n holography for cones

We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography can be obtained by taking the zero-volume limit of holographic defect CFT. Remarkably, it can be regarded as a holographic dual of the edge modes on the defects. For one class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the same for the two theories. In general, cone holography and AdS/CFT are different due to the infinite towers of massive Kaluza-Klein modes on the branes. We test cone holography by studying Weyl anomaly, Entanglement/R\'enyi entropy and correlation functions, and find good agreements between the holographic and the CFT results. In particular, the c-theorem is obeyed by cone holography. These are strong supports for our proposal. We discuss two kinds of boundary conditions, the mixed boundary condition and Neumann boundary condition, and find that they both define a consistent theory of cone holography. We also analyze the mass spectrum on the brane and find that the larger the tension is, the more continuous the mass spectrum is. The cone holography can be regarded as a generalization of the wedge holography, and it is closely related to the defect CFT, entanglement/R\'enyi entropy and AdS/BCFT(dCFT). Thus it is expected to have a wide range of applications.

Minimal SU(5) asymptotic grand unification

We present a minimal model of asymptotic grand unification based on an $SU(5)$ gauge theory in a compact $S^1/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orbifold. The gauge couplings run to a unified fixed point in the UV, without supersymmetry. By construction, fermions are embedded in different $SU(5)$ bulk fields. As a consequence, baryon number is conserved, thus preventing proton decay, and the lightest Kaluza-Klein tier consists of new states that cannot decay into standard model ones. We show that the Yukawa couplings can be either in the bulk or localized, and run to an asymptotically free fixed point in the UV. The lightest massive state can play the role of Dark Matter, produced via baryogenesis, for a Kaluza-Klein mass of about $2.4$ TeV.

Solar axions in large extra dimensions

The axion could be used as a probe for extra dimensions. In large extra dimensions, besides the QCD axion one obtains an infinite tower of massive Kaluza-Klein (KK) states. We describe the processes of KK axions production in the Sun via the axion-photon coupling, gaγγ , and we derive the number density of KK axions that get trapped into the solar gravitational field and then accumulate over cosmic times. The large multiplicity of states, as well as their masses in the keV-range, deeply alter the phenomenology of the axion. This scenario leads us to propose the presence of KK axions as an interpretation of the non-thermal distribution of the solar X-rays. In this work, we dedicate special attention on the astrophysical and cosmological bounds that apply to the model. In particular, we show how the KK axions may escape the EBL limit that constrains standard ALPs in the same mass range. Present searches for KK axions make use of the decay channel, a → γγ, for which we revise the event rate; our value lies orders of magnitude below the rate usually quoted in the literature. This major conclusion stems from recent measurements of the luminosity of the quiet Sun which acts as an irreducible limit. The revised model remains a viable and an attractive explanation for multiple astrophysical observations, and we propose several approaches to search for solar KK axions in the near future.

Warp factor and the gravitational wave spectrum

A distinct signature of compact extra dimensions would be a Kaluza-Klein tower of gravitational waves. Motivated by this prospect, we compute the corresponding spectrum on a warped toroidal background. We evaluate in particular the impact of the warp factor on the spectrum. To that end, we use the complete warp factor H of standard string compactifications, generated by D-branes and orientifolds, thus connecting to recent works on stringy de Sitter constructions. The problematic region close to an orientifold where H < 0 leads to unphysical tachyonic modes in the spectrum. We develop tools that overcome this difficulty and lead to a tachyon-free spectrum. We show, in particular, that the warp factor can lower the first Kaluza-Klein mass by at least 69%.