Can LHC falsify String Theory?

The paper Falsifying Models of New Physics via WW Scattering by Jacques Distler et al. has appeared online in Physical Review Letters. On this occasion the authors prepared a hillarious press release, which gives an impression that the LHC could falsify string theory. This was deservedly laughed off on Not Even Wrong. But the paper itself does not deserve to be scorned. Its topic - UV/IR connections in quantum field theory - is for me one of the most interesting theoretical developments in 2006. Therefore I feel like explaining what this paper is really about. You may say that i'm trying to save the authors from themselves ;-)

I will make the short story long and I will give a less-than-expert level introduction into the subject. Still, I will speak the quantum field theory language. If you're not familiar with this jargon, or just impatient, you are welcome to jump directly to the bottom line.

The most important thing that Papa Weinberg taught us is that the world can be conveniently described by effective quantum field theories. An effective theory is an antonym for the theory of everything. Effective theories have a modest goal to describe those degrees of freedom that are relevant at given energies and in a given experimental setup. Two widespread examples: 1) the Standard Model that describes quarks, leptons and gauge bosons in LEP and Tevatron, and 2) the chiral perturbation theory (ChPT) that describes pions below ~1 GeV.

The particles are represented by quantum fields and their interactions by lagrangians. The main organizing principle is symmetry: in an effective lagrangian we include all terms that are consistent with the symmetries we imposed (local SU(3) x SU(2) x U(1) for the Standard Model, non-linerly realized global SU(2) for the ChPT). There is an infinite number of such terms so we classify them according to how much they contribute to scattering amplitudes at energies of interest. The small expansion parameters is the relevant energy over the cut-off scale (the scale at which the effective theory description breaks down). In the Standard Model we start with a renormalizable lagrangian (operators of dimension <= four). We then add higher dimensional operators that could, for example, affect the renormalitable theory predictions for kaon mixing or change the ratio of Z to W mass (no effects of higher-dimensional operators have been found so far, apart from the neutrino masses maybe). A similar procedure applies in the ChPT, but in this case the higher order (four-derivative operators) have actually been measured. In principle, once we know the UV completion of our effective theory we can determine all the coefficients of the effective theory operators. Thus, the effective theory knows about UV. Is it possible to translate general properties of the UV theory into some relations between the coefficients in the effective theory? This question had not been extensively studied before 2006, although it was known that dispersion relations impose constraints on the parameters of the ChPT. Last year the issue was brought to light by Nima Arkani-Hamed et al. in the paper Causality, analyticity and an IR obstruction to UV completion. They argued that there exist constraints which can be understood at a very intuitive level as imposed by causality of the UV theory. Certain higher-dimensional operators, if occuring with a wrong sign, would allow faster-than-light propagation in certain backgrounds. Nima & co. stressed that a discovery of the wrong sign operators in any effective theory would lead to a conclusion that the UV theory is non-causal, unlike quantum field theory or string theory.

Jacques Distler et al. applied this idea to a specific theory: the electroweak chiral lagrangian (EWChL). This is a sorf of ChPT for the electroweak gauge bosons. This would be the right framework to describe gauge interactions at the LHC below the scale of the higgs boson mass (if it is much heavier than 100 GeV). EWChL contains (at the four-derivative level) two operators that modify 2->2 scattering amplitudes of the SM gauge bosons. Jacques&friends found constraints on the coefficients of these operators that follow from dispersion relations. Their bounds seem to be stronger than those derived by the Nima's speed-of-light arguments and it would be nice to understand them a more intuitive level. Violation of these bounds would signal violations of the assumptions that enter into the dispersion relations: analiticity and unitarity of the scattering amplitudes. String theory is expected not to violate these properties.

Can the LHC falsify string theory then? The answer is a resounding no (of course I can never be 100% sure. I also can't exclude that the LHC will see 1 TeV unicorns, but i wouldn't bet much on any of the two). The most important obstacle is the following. There is a general argument that the EWChL cannot be valid up to very high energies. Reason: EWChL predicts that WW scattering amplitudes become non-unitary around 2 TeV. Therefore the UV completion must become manifest below that scale (the UV theory could well be the Standard Model with a higgs boson). It is highly unlikely that bizarre physics at such a low scale does not manifest itself in any low energy experiments (e.g. in electroweak precision observables). If, on the other hand, the UV theory is a normal well-behaved quantum field theory, it would contribute to the coefficients of the EWChL in a way consistent with the bounds and wipe out any possible contribution of non-standard high energy physics.


Bottom line: the LHC is here to investigate the mechanism of electroweak symmetry breaking, not to test string theory. 16 tons weight on top of those who claim otherwise.