Causality, analyticity and an IR obstruction to UV completion

By A. Adams, N. Arkani-Hamed, S. Dubovsky, Alberto Nicolis, R. Rattazzi. 2006

1,075 citations recorded by the source corpus.

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e9b6ffe2b98db84e8207d5becd8ac78167e3dafb

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Citations in the corpus

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Effective string theory revisited (2012, background): “The overall sign is fixed by the positivity (subluminality) constraint on the forward scattering amplitude [26] Mforward = `(2)sc2s(2) .”
Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff (2015, background): “ical peculiarities|if not necessarily pathologies|are the existence of superluminal excitations about certain backgrounds, and the unusual softness of scattering amplitudes at low energies, M 2!2 ˘E6 [38]. Despite not being inconsistencies of the low-energy eective theory itself, the former obstruct”
Generalized flux vacua (2006, neutral): “Whether this question is best resolved by a top-down (landscape [40]) approach of attempting to characterize the most general structure of string theory compactifications, or by a bottom-up (swampland [24, 41]) approach of understanding which four-dimensional theories have”
Analyticity and the holographic S-matrix (2011, background): “However, in the absence of an explicit Lagrangian (and even in its presence [39]) the definition of locality is often rather murky.”
Imperfect Dark Energy from Kinetic Gravity Braiding (2010, background): “This is also accepted by some of the authors of [62], see [34, 56].”
Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity (2014, background): “Subluminality is a necessary precondition for there to exist a standard Wilsonian ultraviolet completion of the action [82].”
Softness and amplitudes’ positivity for spinning particles (2016, background): “(13)We should also stress that, when scattering massless spins higher or equal than 1, the degree of the polynomial bounding the elastic forward amplitude could be higher or equal than s(2) [1]; in such a case one should trivially take the smallest number of even derivatives that allow to discard th”
Cosmological Moduli and the Post-Inflationary Universe: A Critical Review (2015, background): “We refer the reader to [14] for details.”