Arbitrary Spacetime Dimensions Research Articles

EFT asymptotics: the growth of operator degeneracy

We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of S-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series---partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.

Stationary spacetimes with time-dependent real scalar fields

In 1981 Wyman classified the solutions of the Einstein–Klein–Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.

Factorized lightcone expansion of conformal blocks

We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin and the resummations of the large-spin tails of Regge trajectories. The basic integrals for the Lorentzian inversion are given by Wilson functions.

Conformal partial waves in momentum space

The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension d \geq 3d≥3 (including non-integer dd). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in d = 4d=4 dimensions.

L ∞ -algebras of Einstein–Cartan–Palatini gravity

We give a detailed account of the cyclic L∞-algebra formulation of general relativity with a cosmological constant in the Einstein–Cartan–Palatini formalism on spacetimes of arbitrary dimension and signature, which encompasses all symmetries, field equations, and Noether identities of gravity without matter fields. We present a local formulation as well as a global covariant framework, and an explicit isomorphism between the two L∞-algebras in the case of parallelizable spacetimes. By duality, we show that our L∞-algebras describe the complete Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formulation of Einstein–Cartan–Palatini gravity. We give a general description of how to extend on-shell redundant symmetries in topological gauge theories to off-shell correspondences between symmetries in terms of quasi-isomorphisms of L∞-algebras. We use this to extend the on-shell equivalence between gravity and Chern–Simons theory in three dimensions to an explicit L∞-quasi-isomorphism between differential graded Lie algebras, which applies off-shell and for degenerate dynamical metrics. In contrast, we show that there is no morphism between the L∞-algebra underlying gravity and the differential graded Lie algebra governing BF theory in four dimensions.

Six-point conformal blocks in the snowflake channel

We compute d-dimensional scalar six-point conformal blocks in the two possible topologies allowed by the operator product expansion. Our computation is a simple application of the embedding space operator product expansion formalism developed recently. Scalar six-point conformal blocks in the comb channel have been determined not long ago, and we present here the first explicit computation of the scalar six-point conformal blocks in the remaining inequivalent topology. For obvious reason, we dub the other topology the snowflake channel. The scalar conformal blocks, with scalar external and exchange operators, are presented as a power series expansion in the conformal cross-ratios, where the coefficients of the power series are given as a double sum of the hypergeometric type. In the comb channel, the double sum is expressible as a product of two 3F2-hypergeometric functions. In the snowflake channel, the double sum is expressible as a Kampé de Fériet function where both sums are intertwined and cannot be factorized. We check our results by verifying their consistency under symmetries and by taking several limits reducing to known results, mostly to scalar five-point conformal blocks in arbitrary spacetime dimensions.

Scattering equations in AdS: scalar correlators in arbitrary dimensions

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

Universal Constants and Natural Systems of Units in a Spacetime of Arbitrary Dimension

We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. Lévy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and “universal constants” (such as c and ℏ). We show that all of the known “natural” systems of units contain at least one non-universal constant. We discuss the possible consequences of such non-universality, e.g., the dependence of some of these systems on the number of spatial dimensions. In the search for a “fully universal” system of units, we propose a set of constants that consists of c, ℏ, and a length parameter and discuss its origins and the connection to the possible kinematic groups discovered by Lévy-Leblond and Bacry. Finally, we give some comments about the interpretation of these constants.

Kasner branes with arbitrary signature

We present static and time-dependent solutions for the theory of gravity with a dilaton field and an arbitrary rank antisymmetric tensor. The solutions constructed are valid for arbitrary space-time dimensions and signatures.

Limits on stellar structures in Lovelock theories of gravity

We study the bound on the compactness of a stellar object in pure Lovelock theories of arbitrary order in arbitrary spacetime dimensions, involving electromagnetic field. The bound we derive for a generic pure Lovelock theory, reproduces the known results in four dimensional Einstein gravity. Both the case of a charged shell and that of a charge sphere demonstrates that for a given spacetime dimension, stars in general relativity are more compact than the stars in pure Lovelock theories. In addition, as the strength of the Maxwell field increases, the stellar structures become more compact, i.e., the radius of the star decreases. In the context of four dimensional Einstein-Gauss-Bonnet gravity as well, an increase in the strength of the Gauss-Bonnet coupling (behaving as an effective electric charge), increases the compactness of the star. Implications are discussed.

Hypergeometric presentation for one-loop contributing to H → Z γ

Abstract In this paper, new analytic formulas for one-loop contributing to Higgs decay channel $H \rightarrow Z\gamma$ are presented in terms of hypergeometric functions. The calculations are performed by following the technique for tensor one-loop reduction developed in [A. I. Davydychev, Phys. Lett. B 263 (1991) 107]. For the first time, one-loop form factors for the decay process are shown which are valid at arbitrary space–time dimension $d$.

Analytic functional bootstrap for CFTs in d > 1

We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE, (double) lightcone and Regge limits. Compatibility with the crossing equation imposes constraints on the functional kernels which we study in detail. We then introduce two simple classes of functionals. The first class has a simple action on generalized free fields and their deformations and can be used to bootstrap AdS contact interactions in general dimension. The second class is obtained by tensoring holomorphic and antiholomorphic copies of d = 1 functionals which have been considered recently. They are dual to simple solutions to crossing in d = 2 which include the energy correlator of the Ising model. We show how these functionals lead to optimal bounds on the OPE density of d = 2 CFTs and argue that they provide an equivalent rewriting of the d = 2 crossing equation which is better suited for numeric computations than current approaches.

New one-loop formulas for

Based on the method for evaluating one-loop Feynman integrals developed in [A. I. Davydychev, Phys. Lett. B 263 (1991) 107], new analytic results for one-loop contributing to the decay channels are presented. The form factors shown in this paper are valid at arbitrary space-time dimension.

On self-similar axion-dilaton configurations

We explore self-similar collapse solutions to the Einstein-axion-dilaton system in arbitrary spacetime dimensions, which are invariant under spacetime dilation combined with internal SL(2, ℝ) transformations. We set up a numerical formalism, and test it in four and five dimensions, discovering several new families of solutions in the three conjugacy classes of sl(2, ℝ).

On critical exponents for self-similar collapse

We explore systematically perturbations of self-similar solutions to the Einstein-axion-dilaton system, whose dynamics are invariant under spacetime dilations combined with internal \U0001d530\U0001d529(2, ℝ) transformations. The self-similar solutions capture the enticing behavior “critical” systems on the verge of gravitational collapse, in arbitrary spacetime dimensions. Our methods rest on a combination of analytical and numerical tools, apply to all three conjugacy classes of \U0001d530\U0001d529(2, ℝ) transformations and allow accurate estimates of the corresponding Choptuik exponents. It is well known that these exponents depend on the spacetime dimension and on the matter content. Our main result is that they also attain different values, even within a given conjugacy class, for the distinct types of critical solutions that we recently identified in the Einstein-axion-dilaton system.

The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes

By means of a kinematic analysis of tree level graviton amplitudes we find, at least through six points, that the reason of their decomposition as a sum over products of gauge boson amplitudes is on-shell gauge invariance and unitarity. As a by-product of our analysis we find nonlinear relations obeyed by Yang-Mills amplitudes. All our results are valid for arbitrary spacetime dimensions.

Superfluids, vortices and spinning charged operators in 4d CFT

We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions.

Phase transitions in Born-Infeld AdS black holes in D-dimensions

In this paper, we have investigated phase transitions in arbitrary spacetime dimensions for Born-Infeld AdS black holes. The phase transition points are characterised from the divergence of heat capacity of the black hole. Two well established techniques, namely, the Ehrenfest scheme and the Ruppeiner state space geometry approach are used to identify the order of phase transition the black hole undergoes. It is observed that the results obtained from these two methods agree with each other. Our analysis reveals that the phase transition is of second order. It is also observed from the variation of the heat capacity with entropy that the small unstable black hole phase becomes more and more stable with increase in the spacetime dimensions. We speculate that this dependence of the stability of the black hole on the spacetime dimension can put an upper limit to the dimension of spacetime from the physical condition of the improbability of the formation of a small stable black hole. We have also derived a Smarr relation in D-spacetime dimensions using scaling arguments and first law of black hole thermodynamics which includes the cosmological constant and the Born-Infeld parameters as thermodynamic variables.

Hypergeometric representation of one-loop Higgs decay to two photons

In this paper, we derive hypergeometric function representation of one-loop contributing to Higgs decay to two photons in the standard model and its extensions. The calculations are performed at general space–time dimension d. For the first time, analytic results are published for form factors that are valid in arbitrary space–time dimension. Moreover, we confirm against analytic results in previous computations that have been available in space–time dimension d = 4 – 2ϵ at ϵ0 expansions.

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic objects which compute higher-point global (scalar) conformal blocks in arbitrary spacetime dimensions, extending the result for the four-point block, known in the literature as a geodesic Witten diagram, to five- and six-point blocks. The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime. Using the holographic representation of the higher-point conformal blocks and higher-point propagator identities, we develop geodesic diagram techniques to obtain the explicit direct-channel conformal block decomposition of a broad class of higher-point AdS diagrams in a scalar effective bulk theory, with closed-form expressions for the decomposition coefficients. These methods require only certain elementary manipulations and no bulk integration, and furthermore provide quite trivially a simple algebraic origin of the logarithmic singularities of higher-point tree-level AdS diagrams. We also provide a more compact repackaging in terms of the spectral decomposition of the same diagrams, as well as an independent discussion on the closely related but computationally simpler framework over p-adics which admits comparable statements for all previously mentioned results.