4D Minkowski Spacetime Research Articles

Celestial holography and AdS3/CFT2 from a scaling reduction of twistor space

Celestial amplitudes obtained from Mellin transforming 4d momentum space scattering amplitudes contain distributional delta functions, hindering the application of conventional CFT techniques. In this paper, we propose to bypass this problem by recognizing Mellin transforms as integral transforms projectivizing certain components of the angular momentum. It turns out that the Mellin transformed wavefunctions in the conformal primary basis can be regarded as representatives of certain cohomology classes on the minitwistor space of the hyperbolic slices of 4d Minkowski space. Geometrically, this amounts to treating 4d Minkowski space as the embedding space of AdS3. By considering scattering of such on-shell wavefunctions on the projective spinor bundle ℙ\U0001d54a of Euclidean AdS3, we bypass the difficulty of the distributional properties of celestial correlators using the traditional AdS3/CFT2 dictionary and find conventional 2d CFT correlators for the scaling reduced Yang-Mills theory living on the hyperbolic slices. In the meantime, however, one is required to consider action functionals on the auxiliary space ℙ\U0001d54a, which introduces additional difficulties. Here we provide a framework to work on the projective spinor bundle of hyperbolic slices, obtained from a careful scaling reduction of the twistor space of 4d Minkowski spacetime.

Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics

We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the ``hydrodynamic frame''). We present a class of hydrodynamic frames derived from the relativistic ideal gas ``gamma-law'' equation of state which satisfy the BDNK constraints, and explore the properties of the resulting model for a series of $(0+1)\mathrm{D}$ and $(1+1)\mathrm{D}$ tests in 4D Minkowski spacetime. These tests include a comparison of the dissipation mechanisms in Eckart, BDNK, and M\"uller-Israel-Stewart theories, as well as investigations of the impact of hydrodynamic frame on the causality and stability properties of Bjorken flow, planar shockwave, and heat flow solutions.

Softly higher-derivative massive gravity

In this work, we study the higher-derivative massive gravity in D-dimensional space-time with the mass term arisen due to a 2-brane embedded in a 4D Minkowski spacetime. We consider the effect of a resonance mass term from the DGP braneworld model for the higher-derivative massive gravity. Moreover, we add the gravitational Chern–Simons and Ricci–Cotton terms to this model and evaluate the graviton propagator using a basis of Barnes–Rivers spin projectors. Using the obtained propagator, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity.

Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation

We classified in [1] certain 10d supergravity solutions with a 4d de Sitter, Minkowski or anti-de Sitter spacetime. We then found new solutions in previously unexplored classes. In this paper we study their properties, compare them to swampland conjectures, and make new observations.Using new numerical tools, we first identify all Lie algebras underlying the 6d group manifolds, allowing us to discuss their compactness. We then investigate scale separation, and prove related no-go theorems. Last but not least, we automatize and analyze the stability of all solutions. This leads us to propose the Massless Minkowski Conjecture, claiming the systematic presence of a 4d flat direction.

Scattering Amplitudes: Celestial and Carrollian.

Recent attempts at the construction of holography for asymptotically flat spacetime have taken two different routes. Celestial holography, involving a two dimensional (2D) conformal field theory (CFT) dual to 4D Minkowski spacetime, has generated novel results in asymptotic symmetry and scattering amplitudes. A different formulation, using Carrollian CFTs, has been principally used to provide some evidence for flat holography in lower dimensions. Understanding of flat space scattering has been lacking in the Carroll framework. In this Letter, using ideas from Celestial holography, we show that 3D Carrollian CFTs living on the null boundary of 4D flat space can potentially compute bulk scattering amplitudes. Three-dimensional Carrollian conformal correlators have two different branches, one depending on the null time direction and one independent of it. We propose that it is the time-dependent branch that is related to bulk scattering. We construct an explicit field theoretic example of a free massless Carrollian scalar that realizes some desired properties.

Majorana neutrinos, exceptional Jordan algebra, and mass ratios for charged fermions

Abstract We provide theoretical evidence that the neutrino is a Majorana fermion. This evidence comes from assuming that the standard model and beyond-standard-model physics can be described through division algebras, coupled to quantum dynamics. We use the division algebras scheme to derive mass ratios for the standard model charged fermions of three generations. The predicted ratios agree well with the observed values if the neutrino is assumed to be Majorana. However, the theoretically calculated ratios completely disagree with known values if the neutrino is taken to be a Dirac particle. Towards the end of the article we discuss prospects for unification of the standard model with gravitation if the assumed symmetry group of the theory is E 6, and if it is assumed that space-time is an 8D octonionic space-time, with 4D Minkowski space-time being an emergent approximation. Remarkably, we find evidence that the precursor of classical gravitation, described by the symmetry SU(3)grav × SU(2)R × U(1)grav is the right-handed counterpart of the standard model SU(3)color × SU(2)L × U(1) Y . This provides the theoretical justification for the mass-ratios analysis based on the eigenvalues of the exceptional Jordan algebra.

AdS/QCD oddball masses and the odderon Regge trajectory from a twist-five operator approach

In this work, we consider a massive gauge boson field in ${\mathrm{AdS}}_{5}$ dual to odd glueball states with twist-5 operator in 4D Minkowski spacetime. Introducing an IR cutoff, we break the conformal symmetry of the boundary theory allowing us to calculate the glueball masses with odd spins using Dirichlet and Neumann boundary conditions. Then, from these masses, we construct the corresponding Regge trajectories associated with the odderon. Our results are compatible with the ones in the literature.

Parabolic Verma Modules and Invariant Differential Operators

In the present paper we continue the project of systematic classification and construction of invariant differential operators for non-compact semisimple Lie groups. This time we make the stress on one of the main building blocks, namely the Verma modules and the corresponding parabolic subalgebras. In particular, we start the study of the relation between the parabolic subalgebras of real semisimple Lie algebras and of their complexification. Two cases are given in more detail: the conformal algebra of 4D Minkowski space-time and the minimal parabolics of classical real semisimple Lie algebras.

Double-soft graviton amplitudes and the extended BMS charge algebra

We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of BMS charges on the null boundary. In particular, we show how the commutator of two such charges is realized by the antisymmetrized consecutive soft limit of the double soft amplitude. The commutator is expected to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the Virasoro algebra of local superrotations. We discuss the implications of this structure for the existence of a 2d CFT dual description for 4d scattering amplitudes.

Conformal structure of massless scalar amplitudes beyond tree level

We show that the one-loop on-shell four-point scattering amplitude of massless ϕ4 scalar field theory in 4D Minkowski space time, when Mellin transformed to the Celestial sphere at infinity, transforms covariantly under the global conformal group (SL(2, ℂ)) on the sphere. The unitarity of the four-point scalar amplitudes is recast into this Mellin basis. We show that the same conformal structure also appears for the two-loop Mellin amplitude. Finally we comment on some universal structure for all loop four-point Mellin amplitudes specific to this theory.

Minkowski Flux Vacua of Type II Supergravities.

We study flux compactifications of 10D type II supergravities to 4D Minkowski space-time, supported by parallel orientifold O_{p} planes with 3≤p≤8. With some geometric restrictions, the 4D Ricci scalar can be written as a negative sum of squares involving Bogomol'nyi-Prasad-Sommerfield-like conditions. Setting all squares to zero provides automatically a solution to 10D equations of motion. This way we characterize a broad class, if not the complete set, of Minkowski flux vacua with parallel orientifolds. We conjecture an extension with nongeometric fluxes. None of our results rely on supersymmetry.

Worldline CPT and massless supermultiplets

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the [Formula: see text]-extended superparticle is shown to be anomalous when [Formula: see text] is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral [Formula: see text] gauge invariance. This accords with the fact that no massless [Formula: see text] super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when [Formula: see text] is even, but it has [Formula: see text] states when [Formula: see text] is odd (e.g. the [Formula: see text] hypermultiplet) in contrast to just [Formula: see text] when [Formula: see text] is even (e.g. the [Formula: see text] Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when [Formula: see text] is odd.

Octonionic geometry and conformal transformations

We describe space-time using split octonions over the reals and use their group of automorphisms, the noncompact form of Cartan’s exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of octonionic 8D space with the conformal transformations in 4D Minkowski space-time are studied. It is shown that the dimensional constant needed in these analysis naturally gives the observed value of the cosmological constant.

Conserved higher-spin charges in AdS 4

Gauge invariant conserved conformal currents built from massless fields of all spins in 4d Minkowski space-time and $AdS_4$ are described within the unfolded dynamics approach. The current cohomology associated with non-zero conserved charges is found. The resulting list of charges is shown to match the space of parameters of the conformal higher-spin symmetry algebra in four dimensions.

Yang-Baxter deformations of Minkowski spacetime

We discuss Yang-Baxter sigma deformations of 4D Minkowski spacetime proposed recently. To avoid the degeneracy of the standard bilinear form associated with the familiar coset ISO(1,3)/SO(1,3), we consider a slice of AdS5 in Poincaré coordinates by embedding the 4D Poincaré group into the 4D conformal group SO(2,4). With this procedure we present the metrics and B-fields as Yang-Baxter deformations which correspond to well-known backgrounds such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field.

Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields

Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinatesxμ(withμ=0,1,2,3) and a pair of Grassmannian variables (θ,θ-) which satisfy the standard relationships:θ2=θ-2=0and θθ-+θ-θ=0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian conjugate) without imposing any Hermitian conjugation condition fromoutsideon the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields.

Lax pairs for deformed Minkowski spacetimes

We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical $r$-matrices with Poinca\'e generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincare group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincare group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Spinor fields classification in arbitrary dimensions and new classes of spinor fields on 7-manifolds

A classification of spinor fields according to the associated bilinear covariants is constructed in arbitrary dimensions and metric signatures, generalizing Lounesto's 4D spinor field classification. In such a generalized classification a basic role is played by the geometric Fierz identities. In 4D Minkowski spacetime the standard bilinear covariants can be either null or non-null -- with the exception of the current density which is invariably different from zero for physical reasons -- and sweep all types of spinor fields, including Dirac, Weyl, Majorana and more generally flagpoles, flag-dipoles and dipole spinor fields. To obtain an analogous classification in higher dimensions we use the Fierz identities, which constrain the covariant bilinears in the spinor fields and force some of them to vanish. A generalized graded Fierz aggregate is moreover obtained in such a context simply from the completeness relation. We analyze the particular and important case of Riemannian 7-manifolds, where the Majorana spinor fields turn out to have a quite special place. In particular, at variance with spinor fields in 4D Minkowski spacetime that are classified in six disjoint classes, spinors in Riemannian 7-manifolds are shown to be classified, according to the bilinear covariants: (a) in just one class, in the real case of Majorana spinors; (b) in four classes, in the most general case. Much like new classes of spinor fields in 4D Minkowski spacetime have been evincing new possibilities in physics, we think these new classes of spinor fields in seven dimensions are, in particular, potential candidates for new solutions in the compactification of supergravity on a seven-dimensional manifold and its exotic versions.

De Sitter brane-world, localization of gravity, and the cosmological constant

Cosmological models with a de Sitter 3-brane embedded in a five-dimensional de Sitter spacetime (dS5) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in AdS5 spacetime. Yet there arise a few important differences as compared to the results with a flat 3-brane or 4D Minkowski spacetime. For example, the mass reduction formula (MRF) $M_{Pl}^2=M_{5}^3 \ell_{AdS}$ as well as the relationship $M_{Pl}^2= M_{Pl(4+n)}^{n+2} L^{n}$ (with $L$ being the average size or the radius of the $n$ extra dimensions) expected in models of product-space (or Kaluza-Klein) compactifications get modified in cosmological backgrounds. In an expanding universe, a physically relevant MRF encodes information upon the four-dimensional Hubble expansion parameter, in addition to the length and mass parameters $L$, $M_{Pl}$ and $M_{Pl (4+n)}$. If a bulk cosmological constant is present in the solution, then the reduction formula is further modified. With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{Pl}$ and $M_{Pl (4+n)}$ can be explained in cosmological brane-world models. A notable advantage of having a 5D de Sitter bulk is that in this case the zero-mass wavefunction is normalizable, which is not necessarily the case if the bulk spacetime is anti de Sitter. In spacetime dimensions $D\ge 7$, however, the bulk cosmological constant $\Lambda_b$ can take either sign ($\Lambda_b <0$, $=0$, or $>0$). The D=6 case is rather inconclusive, in which case $\Lambda_b$ may be introduced together with 2-form gauge field (or flux).