arXiv subjects
Publications and source records attributed to Tomasz R. Taylor.
We study three-gluon scattering amplitudes in global de Sitter spacetime, in the angular momentum basis of SO(1,4) symmetry representations. At the tree level, they are determined by the intertwiner integrals of harmonic one-forms on the three-sphere. We derive a general formula valid for all helicity configurations of incoming and outgoing gluons and express the amplitudes in terms of Wigner 3j symbols.
We discuss the symmetry aspects of quantum field theory in global four-dimensional de Sitter spacetime linked to $SO(1,4)$ isometries. For the unitary irreducible representations relevant to elementary particles, we obtain explicit transformation laws for the symmetry generators acting on one-particle states in a basis adapted to the $SU(2) \times SU(2)'$ decomposition of the Hilbert space. Using these results, we derive the corresponding Ward identities and demonstrate how global spacetime symmetries constrain de Sitter scattering amplitudes. We show that the Poincaré algebra and flat-space Ward identities are recovered in the large-momentum limit.
We apply the S-matrix formalism developed in Part I to the interacting scalar theory in four-dimensional de Sitter spacetime. The amplitudes are computed in the angular momentum basis, appropriate to the representations of $SO(1,4)$ de Sitter symmetry group. We discuss the properties of wavefunctions in Bunch-Davies vacuum and derive a new integral representation for the Feynman propagator. We focus on deep infrared processes probing the large scale structure of spacetime, in particular on the processes that are normally forbidden by the energy-momentum conservation laws in flat spacetime. We find that there are no stable particles in self-interacting scalar field theory, but the decay rates are exponentially suppressed for particles with masses far above $\hbar/c\ell$, where $\ell$ is the de Sitter radius. We also show that the ``all out'' amplitudes describing multiparticle production from the vacuum are identically zero, hence Bunch-Davies vacuum is stable with respect to the matter interactions. We show that at the tree level, all scattering amplitudes are infrared finite, well-defined functions of quantum numbers. They have no kinematic singularities, except for the processes involving conformally coupled scalars.
We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link the Hilbert space to geodesic observers. The positive and negative ``energy'' wavefunctions are uniquely determined by the requirement that in observer's neighborhood, short wavelengths propagate as plane waves with positive and negative frequencies, respectively; they define a unique ``Euclidean'' (a.k.a.\ Bunch-Davies) de Sitter invariant vacuum, common to all inertial observers. By following the same steps as in Minkowski spacetime, we show that the scattering amplitudes are given by a generalized Dyson's formula. Compared to the flat case, they describe the scattering of wavepackets with the frequency spectrum determined by geometry. The frequency spread shrinks as the masses and/or momenta become larger than the curvature scale. Asymptotically, de Sitter amplitudes agree with the amplitudes evaluated in Minkowski spacetime.
Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.
Carrollian holography is supposed to describe gravity in four-dimensional asymptotically flat space-time by the three-dimensional Carrollian CFT living at null infinity. We transform superstring scattering amplitudes into the correlation functions of primary fields of Carrollian CFT depending on the three-dimensional coordinates of the celestial sphere and a retarded time coordinate. The power series in the inverse string tension is converted to a whole tower of both UV and IR finite descendants of the underlying field-theoretical Carrollian amplitude. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level. We also discuss the limit of infinite retarded time coordinates, where the string world-sheet becomes celestial.
It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ algebra of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra generating $ SO(1,4)$ or $SO(2,3)$ symmetry groups of $\text{dS}_4$ or $\text{AdS}_4$, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed $\mathrm{w_{1+\infty}}$ are also discussed.
We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find $b^2= (8π^2)^{-1}β_0 \,g^2(M)$, where $b$ is the Liouville coupling constant, $g(M)$ is the Yang Mills coupling at the renormalization scale $M$ and $β_0$ is the one-loop coefficient of the Yang-Mills beta function.
We discuss supersymmetric Yang-Mills theory coupled to dilatons in the framework of celestial holography. We show that in the presence of point-like dilaton sources, the CCFT operators associated with the gauge supermultiplet acquire a simple, factorized form. They factorize into the holomorphic (super)current part and the exponential "light" operators of Liouville theory, in the infinite central charge limit. The current sector exhibits (1,0) supersymmetry, thus implementing spacetime supersymmetry in CCFT.
We consider Yang-Mills theory with the coupling constant and theta angle determined by the vacuum expectation values of a dynamical (complex) dilaton field. We discuss the tree-level N-gluon MHV scattering amplitudes in the presence of a nontrivial background dilaton field and construct the corresponding celestial amplitudes by taking Mellin transforms with respect to the lightcone energies. In this way, we obtain two-dimensional CFT correlators of primary fields on the celestial sphere. We show that the celestial Yang-Mills amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the "light" Liouville operators. They are evaluated in the semiclassical limit of Liouville theory (the limit of infinite central charge) and are determined by the classical Liouville field describing metrics on the celestial sphere.
We discuss the properties of recently constructed "single-valued" celestial four-gluon amplitudes. We show that the amplitude factorizes into the "current" part and the "scalar" part. The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Kač-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. The scalar part can be also obtained by a dimensional reduction of a single D=4 conformal block and the shadow block from Minkowski space to the celestial sphere.
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 $\sim 10^{-1}$.
In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multi-gluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the four-gluon single-valued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the Yang-Mills sector of CCFT.
We demonstrate that the discrepancy between the anomalous magnetic moment measured at BNL and Fermilab and the Standard Model prediction could be explained within the context of low-scale gravity and large extra-dimensions. 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. We show that the KK contribution to $(g-2)_μ$ is universal with the string scale entering as an effective cutoff. The KK tower provides a unequivocal distinctive signal which will be within reach of the future muon smasher.
In a recent paper, here referred to as part I, we considered the celestial four-gluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is ill-defined because it contains branch points related to the presence of conformal blocks with complex spin. In this work, we adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is "soft." By following the approach of Dotsenko and Fateev, we obtain an integral representation of such a single-valued correlator. This allows inverting the shadow transform and constructing a single-valued celestial four-gluon amplitude. This amplitude is drastically different from the original Mellin amplitude. It is defined over the entire complex plane and has correct crossing symmetry, OPE and bootstrap properties. It agrees with all known OPEs of celestial gluon operators. The conformal block spectrum consists of primary fields with dimensions $Δ=m+i λ$, with integer $m\geq 1$ and various, but always integer spin, in all group representations contained in the product of two adjoint representations.
Very recently, the Muon $g-2$ experiment at Fermilab has confirmed the E821 Brookhaven result, which hinted at a deviation of the muon anomalous magnetic moment from the Standard Model (SM) expectation. The combined results from Brookhaven and Fermilab show a difference with the SM prediction $δa_μ= (251 \pm 59) \times 10^{-11}$ at a significance of $4.2σ$, strongly indicating the presence of new physics. Motivated by this new result we reexamine the contributions to the muon anomalous magnetic moment from both: (i)~the ubiquitous $U(1)$ gauge bosons of D-brane string theory constructions and (ii)~the Regge excitations of the string. We show that, for a string scale ${\cal O} ({\rm PeV})$, the contribution from anomalous $U(1)$ gauge bosons which couple to hadrons could help to reduce (though not fully eliminate) the discrepancy reported by the Muon $g-2$ Collaboration. Consistency with null results from LHC searches of new heavy vector bosons imparts the dominant constraint. We demonstrate that the contribution from Regge excitations is strongly suppressed as it was previously conjectured. We also comment on contributions from Kaluza-Klein (KK) modes, which could help resolve the $δa_μ$ discrepancy. In particular, we argue that for 4-stack intersecting D-brane models, the KK excitations of the $U(1)$ boson living on the lepton brane would not couple to hadrons and therefore can evade the LHC bounds while fully bridging the $δa_μ$ gap observed at Brookhaven and Fermilab.
In celestial conformal field theory, gluons are represented by primary fields with dimensions $Δ=1+iλ$, $λ\in\mathbb{R}$ and spin $J=\pm 1$, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are "compatible" in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions $Δ=2+M+iλ$, where $M\ge 0$ is an integer, with integer spin $J=-M,-M+2,\dots,M-2,M$. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.
We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang-Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional supersymmetry algebra. The algebra of $\mathfrak{sbms}_4$ generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.