Flat Space-time Theory Research Articles

Degenerate higher-order Maxwell theories in flat space-time

We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts.

Unconstrained Lagrangian formulation for bosonic continuous spin theory in flat spacetime of arbitrary dimension

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ, similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature.

4D supersymmetric gauge theories of spacetime translations

The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local spacetime translations and supersymmetries generated by transformations whose commutators contain infinitesimal local spacetime translations. Several new supersymmetric free field theories are found which may provide theories of that type. It is outlined how these free field theories may be extended to globally supersymmetric theories with the desired properties. One class of such theories is constructed explicitly. These theories are similar to globally supersymmetric Yang-Mills theories in flat spacetime but have supersymmetries generated by transformations whose commutators generate infinitesimal general coordinate transformations with field dependent gauge parameters.

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar theory * *Supported by the National Key R&D Program of China (2020YFC2201400), the Natural Science Foundation of China (11805083, 11905083, 12005077) and Guangdong Basic and Applied Basic Research Foundation (2021A1515012374)

We study the linear instability and nonlinear dynamical evolution of the Reissner-Nordström (RN) black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime. We focus on the coupling function , which facilitates both scalar-free RN and scalarized black hole solutions. We first present the evolution of system parameters during dynamic scalarization. For parameter regions in which spontaneous scalarization occurs, we observe that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times. At late times, the nonlinear evolution can be considered to be the perturbation of scalarized black holes.

Entanglement in Unruh, Hawking, and Cherenkov radiation from a quantum optical perspective

Free quantum field theory in flat space-time is often believed to be well established, holding no surprises. We hope, by the end of this paper, to have demonstrated that surprises still exist. For example, we will show that a uniformly accelerated atom in Minkowski space-time emits entangled photon pairs in a squeezed state which mimics entanglement of the Minkowski vacuum in that the entanglement is between Minkowski modes which are dominantly in opposite causal wedges of the space-time. Similar emission of photon pairs occurs if an atom is held above the black hole event horizon. Namely, a ground-state atom becomes excited by emitting a ``negative'' -energy photon under the horizon and then spontaneously decays back to the ground state by emitting a positive-energy photon outside the horizon, which propagates away from the black hole.

Aspects of Nonrelativistic Strings

We review recent developments on nonrelativistic string theory. In flat spacetime, the theory is defined by a two-dimensional relativistic quantum field theory with nonrelativistic global symmetries acting on the worldsheet fields. This theory arises as a self-contained corner of relativistic string theory. It has a string spectrum with a Galilean dispersion relation, and a spacetime S-matrix with nonrelativistic symmetry. This string theory also gives a unitary and ultraviolet complete framework that connects different corners of string theory, including matrix string theory and noncommutative open strings. In recent years, there has been a resurgence of interest in the non-Lorentzian geometries and quantum field theories that arise from nonrelativistic string theory in background fields. In this review, we start with an introduction to the foundations of nonrelativistic string theory in flat spacetime. We then give an overview of recent progress, including the appropriate target-space geometry that nonrelativistic strings couple to. This is known as (torsional) string Newton–Cartan geometry, which is neither Lorentzian nor Riemannian. We also give a review of nonrelativistic open strings and effective field theories living on D-branes. Finally, we discuss applications of nonrelativistic strings to decoupling limits in the context of the AdS/CFT correspondence.

Weyl covariance and the energy momentum tensors of higher-derivative free conformal field theories

Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is brute-force and highlights the complexity of the energy momentum tensors, while the second displays some features of their geometric origin as variations of Weyl invariant curved-space actions. New compact expressions for energy momentum tensors are given and specific obstructions to defining them as conformal primary operators in some spacetime dimensions are highlighted. Our discussion is also extended to higher-derivative free spinor theories, which are based on higher-derivative generalizations of the Dirac action and provide interesting examples of conformal field theories in dimension higher than two.

Generalized Maxwell–Higgs vortices in models with enhanced symmetry

Topological vortices in relativistic gauge theories in flat three-dimensional spacetime are investigated. We consider the symmetry mathrm {U(1)}times cdots times mathrm {U(1)}, and for each mathrm {U(1)} subgroup, a complex scalar field transforming under its action is introduced, as well as generalized permeabilities through which the subsystems are coupled. We investigate in detail the features of static, finite energy solutions within this class of generalized Maxwell–Higgs models, and study the effect of the winding numbers in the magnetic properties of each subsystem. A BPS bound and the related first order equations are introduced for a large class of models. Finally, we present some specific models and solve their equations of motion to find solutions engendering many distinct features in relation to each other and to the standard Nielsen–Olesen vortex.

Celestial OPEs and w1+\u221e algebra from worldsheet in string theory

Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with mathcal{N} = 1 and mathcal{N} = 2 worldsheet supersymmetry. In the case of mathcal{N} = 2 string, we also derive all the overline{mathrm{SL}left(2,mathbb{R}right)} descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.

Probing the post-Minkowskian approximation using recursive addition of self-interactions

We address the problem of deriving the post-Minkowskian approximation, widely used in current gravitational wave literature by investigating a possible deduction out of the recursive N\"other coupling approach, from the Pauli-Fierz spin-2 theory in flat spacetime. We find that this approach yields the post-Minkowskian approximation correctly to the first three orders, without invoking any weak-field limit of general relativity. This connection thus establishes that the post-Minkowskian approximation has a connotation independent of a weak-field expansion of general relativity, which is the manner usually presented in the literature. As a consequence, a link manifests between the recursive N\"other coupling approach to deriving general relativity from a linear spin-2 theory in flat spacetime and theoretical analyses of recent detection of gravitational wave events.

On Lorentz-invariant spin-2 theories

We construct Lorentz-invariant massless/massive spin-2 theories in flat spacetime. Starting from the most generic action of a rank-2 symmetric tensor field whose Lagrangian contains up to quadratic in first derivatives of a field, we investigate the possibility of new theories by using the Hamiltonian analysis. By imposing the degeneracy of the kinetic matrix and the existence of subsequent constraints, we classify theories based on the number of degrees of freedom and constraint structures and obtain a wider class of Fierz-Pauli theory as well as massless and partially massless theories, whose scalar and/or vector degrees of freedom are absent. We also discuss the relation between our theories and known massless and massive spin-2 theories.

HS in flat spacetime: the effective action method

This is the first paper in a series of three dealing with HS theories in flat spacetime. It is divided in three parts. The first part is an elaboration on the method of effective action, initiated in a previous paper. We study the properties of correlators of currents in the free fermion coupled to external higher spin (HS) potentials, and develop techniques for their explicit calculation. In particular we show how they can be calculated via ordinary Feynman diagram techniques. We also introduce the concept of curvedL_infty algebra and show how it can be realized in the context of the fermion model. In part II we compare the results of the scalar model and those of the fermion model (coupled to HS fields). We show that the HS field formulation coming from the scalar model is the ‘square’ of the one ensuing from the fermion model. Finally, in part III, we analyse the possible obstructions that one may meet in constructing the effective action: these are the analogues of anomalies in ordinary gauge theories. We provide explicit and compact formulas of the latter.

Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes

The local free action principle for bosonic unconstrained higher spin gauge fields in $d$-dimensional (A)dS$_d$ spacetime has been already established by Segal. However, later on, Schuster and Toro, in 4-dimensional flat spacetime, extracted such an action from their bosonic continuous spin gauge theory, when the continuous spin parameter vanishes. On the other hand, similar to the Schuster-Toro's action, we found the fermionic continuous spin gauge theory in 4-dimensional flat spacetime. Thus it is noteworthy to take out its fermionic higher spin formulation in a limit, and generalize it to $d$-dimensional (A)dS$_d$ spacetime. Therefore, in this paper, we will present a similar action principle \`a la Segal for fermions in $d$-dimensional (A)dS$_d$ spacetime. Moreover, at the level of equations of motion, we will demonstrate how the Fronsdal and the Fang-Fronsdal equations in $d$-dimensional (A)dS$_d$ spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.

Nonrelativistic string theory and T-duality

Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.

Absence of cosmological constant problem in special relativistic field theory of gravity

The principles of quantum field theory in flat spacetime suggest that gravity is mediated by a massless particle with helicity ±2, the so-called graviton. It is regarded as textbook knowledge that, when the self-coupling of a particle with these properties is considered, the long-wavelength structure of such a nonlinear theory is fixed to be that of general relativity. However, here we indicate that these arguments conceal an implicit assumption which is surreptitiously motivated by the very knowledge of general relativity. This is shown by providing a counterexample: we revisit a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free helicity ±2 graviton. We explicitly prove that this theory, known as Weyl-transverse gravity (unimodular gravity with explicit Weyl invariance), can be understood as the result of self-coupling in complete parallelism to the well-known case of general relativity. We discuss the absence of cosmological constant problem in this theory, highlighting that it provides a particular realization of previous arguments formulated in studies of the emergence of the gravitational interaction from condensed-matter-like models. Overall, we conclude that the consideration that gravity is mediated by a massless particle with helicity ±2 does not inextricably lead to the cosmological constant problem.

Scalar charges and the first law of black hole thermodynamics

We present a variational formulation of Einstein–Maxwell-dilaton theory in flat spacetime, when the asymptotic value of the scalar field is not fixed. We obtain the boundary terms that make the variational principle well posed and then compute the finite gravitational action and corresponding Brown–York stress tensor. We show that the total energy has a new contribution that depends on the asymptotic value of the scalar field and discuss the role of scalar charges for the first law of thermodynamics. We also extend our analysis to hairy black holes in Anti-de Sitter spacetime and investigate the thermodynamics of an exact solution that breaks the conformal symmetry of the boundary.

Nonrelativistic trace and diffeomorphism anomalies in particle number background

Using the heat kernel method, we compute nonrelativistic trace anomalies for Schr\"odinger theories in flat spacetime, with a generic background gauge field for the particle number symmetry, both for a free scalar and a free fermion. The result is genuinely nonrelativistic, and it has no counterpart in the relativistic case. Contrary to naive expectations, the anomaly is not gauge invariant; this is similar to the nongauge covariance of the non-Abelian relativistic anomaly. We also show that, in the same background, the gravitational anomaly for a nonrelativistic scalar vanishes.

Thermal bath in de Sitter space from holography

We consider the AdS/dS CFT correspondence and study the nature of the thermal bath of the de Sitter field theory using holography. Unlike the temperature of a thermal field theory in flat spacetime, the temperature of a superconformal field theory on de Sitter space is an integral part of the theory and leaves intact the conformal symmetry and supersymmetry. In the dual AdS side, there is no black hole. Instead we have cosmological expansion of the de Sitter factor. We consider a number of different observables, such as the entanglement entropy, two point correlation function, Wilson loops corresponding to static and spinning mesons in the field theory, and study their thermal properties using holography. The former two quantities have trivial temperature dependence due to conformal symmetry. We compute the energy of the quark anti-quark bound state for a static meson, as well as the energy and the angular momentum for a spinning meson. We find that there is a maximum distance, as well as a maximum spin for the latter case, beyond which the bound state become unstable. The temperature behavior of the physical quantities in these meson systems are similar to that of the usual thermal field theory with holographic black hole dual. With these examples, we show clearly how the field theory observables get their thermal properties from the bulk despite the absence of a black hole, with the role of the black hole horizon played by the cosmological expansion of the de Sitter factor of the AdS metric.

Averaged null energy condition from causality

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, ∫ duTuu, must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to n-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form ∫ duXuuu···u ≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

Higher derivative corrections to the DBI action at α′2 order

We use the compatibility of D-brane action with linear off-shell T-duality and linear on-shell S-duality as guiding principles to find all world volume couplings of one massless closed and three massless open strings at order $\alpha'^2$ in type II superstring theories in flat space-time.