Comments on Unparticles

By B. Grinstein, K. Intriligator, I. Rothstein. 2008

190 citations recorded by the source corpus.

Abstract We comment on several points concerning unparticles which have been overlooked in the literature. One regards Mack's unitarity constraint lower bounds on CFT operator dimensions, e.g., d V ⩾ 3 for primary, gauge invariant, vector unparticle operators. We correct the results in the literature to account for this, and also for a needed correction in the form of the propagator for vector and tensor unparticles. We show that the unitarity constraints can be directly related to unitarity requirements on scattering amplitudes of particles, e.g., those of the Standard Model, coupled to the CFT operators. We also stress the existence of explicit Standard Model contact terms, which are generically induced by the coupling to the CFT (or any other hidden sector), and are subject to LEP bounds. Barring an unknown mechanism to tune away these contact interactions, they can swamp interference effects generated by the CFT. We illustrate these points in the context of a weakly coupled CFT example. A significant amount of the unparticle literature should be reconsidered or revised in light of the observations in this note.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/96726e6141e89c3501d76ca34f791fe644ff5c11

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In Nuclear and High Energy Physics

Citations in the corpus

Minimal conformal technicolor and precision electroweak tests (2010, background): “Unitarity implies d ≥ 1, and in the limit d → 1 the correlation functions of the operator becomes those of a free scalar [48, 49].”
Convexity and liberation at large spin (2012, background): “A classic result is that, in unitarity CFTs, operators obey the so-called unitarity bounds [12] (see also [13]).”
Bootstrapping the O(N ) vector models (2013, background): “Further, in D-dimensional unitary theories the operator dimensions must satisfy the lower bounds [35–39] ∆ ≥ {”
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, unknown): “Primaries in reflection positive (or unitary) CFTs are known to have non-negative anomalous dimensions [11, 38–41]: ∆ ≥ D/2− 1 (l = 0) , ∆ ≥ l +D − 2 (l ≥ 1) .”
What Maxwell Theory in D 4 teaches us about scale and conformal invariance (2011, background): “We will give here an independent derivation of this result (see [26], [4] for similar arguments) based on the fact that conformal invariance fixes the primary vector two-point function to have the (Euclidean) form:”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, background): “…the positivity of the Fourier transform of the 2pt function analytically continued to Lorentzian signature (the Wightman function), see Ferrara et al. (1974a), Mack (1977a) (in the sufficiency part of the argument), as well as Grinstein et al. (2008) for a recent exposition emphasizing physics.”
Ground states of holographic superconductors (2009, background): “1 If ∆Φ > 3, then the operator J0 dual to Φ is also an irrelevant perturbation, so again one has a sensible field (1)Also, there is a unitarity bound ∆Φ ≥ 2 for gauge-invariant, primary operators [18] (see also [19]), suggesting that even in a more general setup, one cannot have m(2)Φ < 0.”
Bounding scalar operator dimensions in 4D CFT (2008, background): “Recently [ 17 ], some of these bounds were rederived in a very physically transparent way, by weakly coupling a free scalar theory to the CFT and studying the unitarity of the S-matrix generated by exchanges of CFT operators.”