Massive Spin-two Field Research Articles

Cheeger bounds on spin-two fields

We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The argument involves a recently-noticed relation to Bakry-Émery geometry, a version of the so-called Cheeger constant, and the theory of synthetic Ricci lower bounds. The latter technique allows generalizations to non-smooth spaces such as those with D-brane singularities. For AdSd vacua with a bridge admitting an AdSd+1 interpretation, the holographic dual is a CFTd with two CFTd−1 boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for d = 4. We also prove new bounds on the higher eigenvalues. These are in agreement with the spin-two swampland conjecture in the regime where the background is scale-separated; in the opposite regime we provide examples where they are in naive tension with it.

Higuchi bound on slow-roll inflation and the swampland

In this paper we study the implications of the generalized Higuchi bound on massive spin-two fields for the derivative of the scalar potential within bimetric theory. In contrast to the recent de Sitter swampland conjecture, an upper bound on the derivate of the scalar potential follows from the generalized Higuchi bound. In combination, this leaves a window for the derivate of the scalar potential. We discuss this bound in several representative bimetric models and parameter regions.

Looking for partially-massless gravity

We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that the gauge and parity invariant interaction of PM spin two particles requires the inclusion of specific massive spin-two fields and leads to a reconstruction of Conformal Gravity, or multiple copies of the latter in even dimensions. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but this theory cannot be constructed in the standard formulation, due to the absence of the parity-odd cubic vertex therein. Finally, by relaxing the general covariance, we show that a “non-geometric” coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory. We also clarify some aspects of interactions between massless, partially-massless and massive fields, and resolve disagreements in the literature.

A string theory which isn\u2019t about strings

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct ab initio quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in D = 26 factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.

Self-interacting charged massive spin two particles in Minkowski spacetime

A model of the self-interacting charged massive spin-two field is constructed. We investigate several properties of the model and find that the trivial vacuum is only allowed due to the internal symmetry. This suggests that the Higgs mechanism might not be induced by the model of the massive spin-two field with the ghost-free potential.

Renormalizable toy model of massive spin-two field and new bigravity

In this paper, we propose a toy model of the renormalizable theory describing massive spin two field. Although the model is renormalizable, we show that the model contains ghost. The coupling of the theory with gravity can be regarded as a new kind of bimetric gravity or bigravity. We show that the massive spin two field plays the role of the cosmological constant.

Pomeranchuk instability in a non-Fermi liquid from holography

The Pomeranchuk instability, in which an isotropic Fermi surface distorts and becomes anisotropic due to strong interactions, is a possible mechanism for the growing number of experimental systems which display transport properties that differ along the $x$ and $y$ axes. We show here that the gauge-gravity duality can be used to describe such an instability in fermionic systems. Our holographic model consists of fermions in a background which describes the causal propagation of a massive neutral spin-two field in an asymptotically AdS spacetime. The Fermi surfaces in the boundary theory distort spontaneously and become anisotropic once the neutral massive spin-two field develops a normalizable mode in the bulk. Analysis of the fermionic correlators reveals that the low-lying fermionic excitations are non-Fermi liquid-like both before and after the Fermi surface shape distortion. Further, the spectral weight along the Fermi surface is angularly dependent and can be made to vanish along certain directions.

Massive Gravity theories and limits of ghost-free bigravity models

Abstract We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic c-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic c-theorems.

(De)quantization of black hole charges

We argue that magnetic and electric charges of the Reissner–Nordström black hole are quantized in CP conserving theories. A dequantization phenomenon occurs when CP is broken either explicitly or effectively, and, as a result, pure magnetic black holes are not possible. Two examples illustrating this phenomenon are discussed. One is the electric charge induced by the neutral pion field in a magnetically charged black hole, and another is the electric charge induced due to the massive spin-two field emerging from possible higher curvature terms.

ACTION FOR (FREE) OPEN STRING MODES IN AdS SPACE USING THE LOOP VARIABLE APPROACH

The loop variable technique (for open strings in flat space) is a gauge-invariant generalization of the renormalization group method for obtaining equations of motion. Unlike the beta functions, which are only proportional to the equations of motion, here it gives the full equation of motion. In an earlier paper, a technique was described for adapting this method to open strings in gravitational backgrounds. However, unlike the flat space case, these equations cannot be derived from an action and are therefore not complete. This is because there are ambiguities in the method that involve curvature couplings that cannot be fixed by appealing to gauge invariance alone but need a more complete treatment of the closed string background. An indirect method to resolve these ambiguities is to require symmetricity of the second derivatives of the action. In general this will involve modifying the equations by terms with arbitrarily high powers of curvature tensors. This is illustrated for the massive spin-two field. It is shown that in the special case of an AdS or dS background, the exact action can easily be determined in this way.

Virasoro invariance and theory of internal string.

Treating the Virasoro invariance of the string as an internal symmetry, we show how to construct gauge theories of the Virasoro group which could be interpreted as a theory of an internal string. To do this we first generalize the Kaplansky-Feigin-Fuks representation of the Virasoro algebra, and construct the invariant tensors which play the crucial role in gauge theories of the Virasoro group. Next we clarify the geometric meaning of the Kaplansky-Feigin-Fuks representation, and show that any five-dimensional field theory defined on the fiber bundle space made of the four-dimensional space-time and the internal string ${S}^{1}$ which is invariant under the space-time-dependent reparametrization of the string can be interpreted as a gauge theory of the Virasoro group from the four-dimensional point of view. We discuss two types of theories: one in which the space-time metric does not depend on the string coordinate and one in which the space-time metric does. In both cases we show that spontaneous symmetry breaking is possible. In the latter case we discuss how spontaneous symmetry breaking can generate an infinite tower of massive spin-two fields, and construct the massive spin-two fields explicitly. We argue that one of the gauge theories could provide a field-theoretic description of a real string, in the point limit of the string.

Explicit construction of massive spin-two fields in Kaluza-Klein theory.

We show how spontaneous breaking of the Virasoro group in the 5-dimensional Kaluza-Klein theory generates an infinite tower of massive spin-two fields. In particular we show explicitly how the massive spin-two fields can be expressed in terms of the helicity \ifmmode\pm\else\textpm\fi{}2, \ifmmode\pm\else\textpm\fi{}1, 0 states. Moreover we prove that the effective Lagrangian reduces exactly to the Pauli-Fierz Lagrangian in the lowest order of the perturbation around the vacuum, when expressed exclusively by the massive spin-two fields.

Theory of Gravity in Fierz Variables (The Linear Case)

We present a complete theory of massive and massless spin-two field using Fierz variables Aαβμ for flat and curved space-times; its relationship with the standard variable Ψμν and the bridge relation which allows the passage from one representation to the other. The theory presented is nothing but the weak approximation of Einstein's General Relativity in the Jordan-Lichnerowicz formulation.

Interacting Lagrangian for massive spin-two field.

As is well known, Kaluza-Klein compactification of five-dimensional gravity gives a four-dimensional theory of a tower of massive spin-2 fields interacting with background gravitational, electromagnetic, and scalar fields. Working to lowest order in the massive fields, one can obtain a Lagrangian for a single massive spin-2 field interacting with gravitational and other background fields which is consistent up to terms of higher order in the massive spin-2 field. This consistency depends on massive spin-2 gauge invariances which are valid up to terms of higher order in the massive field. We explicitly exhibit the four-dimensional Lagrangian and its gauge transformations. This analysis parallels a similar analysis in string theory carried out elsewhere.

Interacting spin-two field on the light front

The minimal (30-component) massive spin-two field is examined from the viewpoint of the Cauchy initial-value problem. The use of light-cone coordinates requires the existence of 25 independent constraints on the system, a number which is shown to obtain if one performs up to three successive differentiations of the primary constraint equations. These manipulations allow one to construct an algorithm for the evaluation of 25 dependent components in terms of a conveniently chosen set of five independent field variables. The introduction of an electromagnetic coupling is shown to result in a loss of some of the required constraint equations with two aspects of this breakdown being noteworthy. These are (a) the fact that (as in the spin-$\frac{3}{2}$ theory) the problem of obtaining the correct degrees of freedom can be solved if the condition ${F}_{\ensuremath{-}i}=0$ is imposed and (b) the loss of constraint occurs at the highest possible level, i.e., in the quaternary constraints rather than at the secondary or tertiary stages of the calculation.

Minimal Electromagnetic Coupling of Spin-Two Fields

The apparent increase in the number of degrees of freedom of a massive spin-two field upon introduction of minimal electromagnetic coupling is considered. It is shown that if one gives up the usual formulation of such a system in favor of one possessing fewer dependent field components such a problem does not occur. It is consequently suggested that minimal coupling may be a useful concept only within the framework of theories which are described with a minimal number of components.

THE MASSIVE SPIN–TWO FIELD

The energy of the free massive spin-two field is exhibited as a manifestly positive-definite function of its canonical variables. The indefiniteness of the form recently obtained by Adler is shown to be only apparent in nature. A summary of the canonical reduction of the theory is given in the Appendix.