String Theory and the Velo–Zwanziger problem

Porrati, Massimo; Rahman, Rakibur; Sagnotti, A.

doi:10.1016/j.nuclphysb.2011.01.007

Cited by 49 publications

(86 citation statements)

References 107 publications

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“…In this limit, an infinite number of higher-spin gauge fields appear and the understanding of consistent higher-spin gauge theories may be very helpful to describe this phase (see e.g. [3][4][5] and refs therein for some recent works).…”

Section: Jhep02(2011)048mentioning

confidence: 99%

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Effective action in a higher-spin background

Bekaert

Joung

Mourad

2011

J. High Energ. Phys.

111

212

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We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.

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Section: Jhep02(2011)048mentioning

confidence: 99%

“…We leave all these issues for a future work. 5 In the literature, this matching is usually performed for the boundary currents and the gauge-fixed bulk fields, see e.g. [12].…”

Section: Jhep02(2011)048mentioning

confidence: 99%

Effective action in a higher-spin background

Bekaert

Joung

Mourad

2011

J. High Energ. Phys.

111

212

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“…[25] One example, in a different context, is the use of string theoretical non-minimal couplings for charged higher spins [20].…”

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confidence: 99%

Acausality of Massive Gravity

2013

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We show that the ghost-free, 5 degree of freedom, Wess-Zumino (1970) massive gravity model is acausal. By analyzing its characteristics, we demonstrate that shock wave solutions exhibit superluminal behavior. Ironically, this pathology arises from the very constraint that removes the Boulware-Deser ghost mode. PACS numbers: INTRODUCTIONOver four decades ago, Isham, Salam and Strathdee proposed a 2-tensor "f -g" theory [1] by adding to the Einstein action that of a second vierbein, f µ m , plus a non-derivative coupling term, leaving a single common coordinate invariance. Of particular interest is the limit of non-dynamical (say flat) f , giving a finite range to the gravitons due to the coupling "mass" term. It was rapidly shown [2] however, that unlike their linearized massive spin 2 Fierz-Pauli (FP) limits, these models suffered from a ghost problem: generic non-linearities reinstate a 6th degree of freedom (DoF), beyond the linearized 2s+1 = 5 DoF, one of which is necessarily ghost-like. A final twist, also from that time, was Wess and Zumino's [3] discovery of a distinguished set of f -g mass terms of which at least one is immune from this disease, keeping 5 DoF. Because [3] was only published without detail in lecture notes, it remained unknown. Separately, other analyses showed that the linearized theory's matter coupling seemed to suffer a "vDVZ" discontinuity [4], as well as a failure of the Birkhoff theorem [5]. Hence, the subject remained moribund until the recent (independent) rediscovery [6] of the results [3] plus two new f -g models. This exhumation has, unsurprisingly, generated an immense industry (see the recent survey [7]). Our purpose is to re-inter f -g. We will show that the first, 5 DoF, Wess-Zumino, model is acausal. Our methods also show that of the two remaining such models [6], one is definitely acausal and the other likely so [8] [23]. Paradoxically, acausalities arise precisely because of the very constraint that removes the ghost. Note that there is no conflict between acausality and ghostlessness, as witness the old "charged" higher (s > 1) spin interactions with Maxwell and gravity, say those of s = (3/2, 2) [13][14][15], that are also invalidated only by acausality.Our results will be obtained by using the method of characteristics, analyzing the constraints' shock wave discontinuities, in particular that of the "5th" scalar one that results from combining the trace and double divergence of the field equations, just as is done in the linear FP model, to find a derivative-free constraint. THE MODEL AND THE FIFTH CONSTRAINTOur concrete 5 DoF model iswhere all indices are moved by the dynamical metric g µν and its associated vierbein e µ m ; in particular f µν is the fixed background vierbein f µ m times e νm , and is manifestly symmetric on-shell. Vanishing of its antisymmetric part yields 6 conditions. Taking the reference f µ m field as the flat bein is a popular choice but is not physically required; in fact, our results, both for acausality and the absence of the sixth ghost mo...

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“…In particular, the cubic vertices of higher spin fields have been constructed in [9,11,13,14,[16][17][18]20,[22][23][24][25][26][27], the cubic vertices for higher spin fields coupled to external electromagnetic and gravitational backgrounds have been elaborated in [28][29][30][31][32][33][34][35]. The quartic approximation of the interaction vertices has been studied much less (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

Buchbinder

Krykhtin

2015

Eur. Phys. J. C

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We consider the massive integer higher spin fields coupled to an external constant electromagnetic field in flat space of arbitrary dimension and find a gauge invariant quartic interaction vertex which is quadratic in a dynamical higher spin field and quadratic in the external field. The construction of the vertex is based on the BRST approach to higher spin field theory where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning (unconstrained formulation).

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String Theory and the Velo–Zwanziger problem

Cited by 49 publications

References 107 publications

Effective action in a higher-spin background

Effective action in a higher-spin background

Acausality of Massive Gravity

Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

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