# Supersymmetry and String Theory

by NeedBranes
Tags: string, supersymmetry, theory
 P: 12 I just recently seen an article that the recent findings at the LHC seem to disprove supersymmetry. I would like to know how supersymmetry and string theory are connected and what the implications would be if the LHC totally disproves supersymmetry all together?
Emeritus
PF Gold
P: 29,238
 Quote by NeedBranes I just recently seen an article that the recent findings at the LHC seem to disprove supersymmetry. I would like to know how supersymmetry and string theory are connected and what the implications would be if the LHC totally disproves supersymmetry all together?
This is why we require that you cite your sources when discussing something like this. I will bet you that it doesn't say that it disproves supersymmetry, but rather, they haven't found anything beyond what the Standard Model predicted from the Bs decay.

Be very careful on interpreting what you read!

Zz.
 P: 12 http://www.scientificamerican.com/ar...-seek-new-idea Sorry, I'm still fairly new at this.
 Astronomy Sci Advisor PF Gold P: 23,235 Supersymmetry and String Theory Hi NB, and Zapper, I also recently saw some articles about the lack of evidence for SUSY at LHC energy levels. For example this was at the Simons Foundation website, it seemed balanced well informed and decently written: https://simonsfoundation.org/feature...eek-new-ideas/ the style was less dramatic, less sensational than, say, the BBC article There was also this in Nature magazine, about the same topic http://www.nature.com/news/truant-pa...mmetry-1.11855 "truant particles turn the screw on supersymmetry" (note slightly jazzier headline) Finally there was the more sensational impressionistic BBC article, where the language is less controlled and can give reader's inaccurate impressions. http://www.bbc.co.uk/news/science-environment-20300100 I think the point is that physics is an experimental/empirical science---they want to explain the nature they can see. If supersymmetry exists only at far higher energies so they can't think of how to observe the effects, then it might exist but can't be seen. So they lose interest and enthusiasm for it. What these journalists are sensing and reporting is not a DISPROOF but more of a loss of interest among researchers in building SUSY models of nature. The game is to build mathematical models of nature that will exhibit visible effects. Otherwise it is more on the level of philosophy.
 Astronomy Sci Advisor PF Gold P: 23,235 Hi NB, I didn't see your post #3 when I was posting. You came up with the same article, by Natalie Wachover, that I did. It was at the Simons news site and the SciAm reprinted it. I think it captures the mood in a balanced way. Not DISPROOF but more like when there is a slow leak in the air of one of the tires on your car. There still are parts of the parameter space they haven't searched thoroughly so something could still turn up at the LHC energy levels, and this trend could be reversed! But if not, the younger theorists will gradually find other areas to go into and other things to work on. I guess. There is a whole world of other stuff for them to investigate.
 Sci Advisor P: 912 Afaik you need targetspace susy to interpret the string spectrum. If susy would fail to be there in nature, string theory would have a hard time I guess. In most texts it's not really treated thoroughly, though. Check greens schwarz witten on this :)
 PF Gold P: 341 The principle that a string should sweep out a world sheet of minimum area leads directly to the Nambu-Goto string action. However, the Nambu-Goto string seemed difficult to quantise. In introductory texts to string theory the Nambu–Goto string is barely mentioned, you almost immediately switch to the Polyakov string whose corresponding action has the same set of classical solutions as the Nambu-Goto action, but is bilinear in basic string variables and so is easier to quantize. However, this switch, from a geometrical point of view, is a rather unnatural reformulation and comes at the price of introducing an additional Weyl invariance and an auxiliary worldsheet metric. The consistency requirements of standard string theory - the need for extra dimensions and supersymmetry - arise from the particular Fock representation of the Polyakov string. In the the paper http://arxiv.org/pdf/hep-th/0401172v1.pdf Thiemann uses rigorous techniques of AQFT and LQG to do a quantization of the Nambu-Goto string and found there is no need for extra dimensions or supersymmetry to make the theory consistent.
 PF Gold P: 341 The world sheet is described by $X^\mu (\sigma , \tau)$, the position of the string for given values of $\sigma$ and $\tau$. The Nambu-Goto action is simply proportional to the area, $S = T \int d \sigma d \tau \sqrt{\dot{X}^2 X^{\prime 2} - (\dot{X} \cdot X')^2}$ where $\dot{X}^\mu = {\partial X^\mu (\sigma , \tau) \over \partial \tau} , \;\;\;\; X^{\prime \mu} = {\partial X^\mu (\sigma , \tau) \over \partial \sigma}.$ this was thought difficult to deal with because it is highly non-linear and especially because of the square root. This action can be rewritten with the introduction of a new variable $h_{\alpha \beta}$, which is a world sheet metric: $S = - {T \over 2} \int d^2 \sigma \sqrt{h} h^{\alpha \beta} \eta_{\mu \nu} \partial_\alpha X^\mu \partial_\beta X^\nu.$ This is the Polyakov action - bilinear. The string action describes a 1+1 dimensional field theory invariant under active diffeomorphisms of the world sheet (for the Nambnu-Goto string this is the only local symmetry), hence the reason why LQG techniques are applicable.
P: 756
 Quote by julian Thiemann uses rigorous techniques of AQFT and LQG to do a quantization of the Nambu-Goto string and found there is no need for extra dimensions or supersymmetry to make the theory consistent.
I would emphatically assert that if you want to do string theory without supersymmetry and extra dimensions, this is not the way to do it. Anyone interested in that should be looking at the original bosonic string, at "type 0 string theory", at "nongeometric" phases of string theory, at "Liouville string theory". These are all variations on the standard superstring which still preserve the defining qualities of the string approach, such as the worldsheet dualities and high-energy behavior which lay behind Veneziano's original formula.

Thiemann's "LQG-string" really has nothing in common with string theory. As explained by Urs Schreiber here in comments #6 and #9, the method of quantization employed already deviates from ordinary QFT (he repeats the point in a comment at Jacques Distler's blog). This is a rather serious point. The history of quantum mechanics is an interplay of theory and experiment. The harmonic oscillator is quantized in a certain way, then fields in the same way, and then finally strings. The strings aren't experimentally validated so far, but the quantum oscillators and the quantum fields certainly have been. But Thiemann's method of quantization throws out all of that and revises even the harmonic oscillator.
 PF Gold P: 341 Are you talking about arguments claiming discontinuous representations do not give physically correct answers? I think Thiemann and others have countered these arguments. Thiemann for example, in his book on quantum general relativity pages 217-218, he argues that the physics of the discontinuous representation is indistinguishable from the physics of the Schrodinger representation within error $\delta$ (which of course includeds the SHO). Its been a while, I need to go through these arguments again. Can I just add that in the quantization of geometric theories there may be good physical reasons for these representations being discontinuous; if spatial geometry takes on a discrete nature upon quantization, it may not be surprising that there exists no operator generating infinitesimal spacial `translations'.
 P: 203 Regarding supersymmetry, am I right in thinking that there's nothing else on the table which comes remotely close to providing a toolkit to handle the hierarchy problem? (Note I'm not claiming that just the existence of supersymmetry provides a complete answer - we also need mechanisms for its partial breaking ).
 P: 756 There are non-susy schemes, like "little Higgs". They too require new particles that aren't showing up. The "SM-only" answer is Shasposhnikov-Wetterich 2009, who even predicted the Higgs mass (!), by assuming that gravity at the Planck scale is "asymptotically safe". I think this behavior is inconsistent with conventional ideas about micro black hole thermodynamics (and virtual micro black holes should be copiously produced at those energies), but the idea of getting the Higgs mass (and stabilizing it) from special high-energy boundary conditions on RG flow obviously deserves a lot more attention. Regarding Thiemann's unconventional method of quantization, I don't know the status of attempts to make it work for ordinary quantum fields, just that from a QFT perspective, it's an example of dangerous tinkering with something that was already working fine. But regarding strings... the worldsheet metric that is introduced, in passing from the Nambu-Goto action to the Polyakov action - rather than being an ugly complication, it's the gateway to everything that makes string theory what it is. The symmetries of the worldsheet implied by the metric are actually what demands a space-time background consistent with general relativity (space-time coordinates of points on the string translate to bosonic fields "on the string", conformal symmetry at the quantum level requires that the beta functions of these fields are zero, and that in turn implies Ricci flatness for the space-time metric). I think it leads to holography too, though I can't quite state that argument. Even if we wanted to talk about noncommutative or nongeometric "strings", I think we would want to preserve the abstract algebraic properties (e.g. of amplitudes) associated with the conformal symmetry, if we wished to regard these new models as connected to the string theory enterprise.
 P: 343 So the on metric on the world sheet is not physical right? It's an auxiliary field introduced to make one's life easier. Then the choice of a flat metric is arbitrary too. Is there then a deeper reason that 2-d conformal field theory plays such an important role in string theory?
P: 912
 Quote by Finbar So the on metric on the world sheet is not physical right? It's an auxiliary field introduced to make one's life easier.
Yes, it is an auxiliary field such that you can get rid of the square root, which is nice for quantization. Its algebraic EOM however say that it is induced by the targetspace (spacetime!) metric. In that sense I wouldn't call it "not physical". For example, if you embed the sphere in flat space, the metric of flat space induces the metric on the sphere. I wouldn't call this metric "unphysical". The difference with string theory is that the worldsheet metric is determined up to a conformal factor because you are in two dimensions, an extremely important fact!

 Then the choice of a flat metric is arbitrary too. Is there then a deeper reason that 2-d conformal field theory plays such an important role in string theory?
Well, what one does is gauge-fix the metric. For this you put constraints on the symmetries, which should preserve the choice of gauge. What happens in ST is that the choice of gauge is preserved by Lorentz transformations, and gct's which induce a Weyl transformation. Ultimately, this is the reason why ST is a 2-dim. CFT.

I would say that it is a counting argument. A metric has 3 components, which can be gauge fixed by 2 gct's and one Weyl rescaling. However, the intersection of Weyl rescalings and gct's is not empty, so you can still perform a Weyl rescaling on the metric and undo the effect on the metric with a gct without messing up the choice of a flat ws-metric. Hence, you have more than just Poincare symmetry for the chosen worldsheet metric. Of course, this phenomena is not unfamiliar; it is very often the case that a choice of gauge doesn't completely fix the gauge freedom one has (think about GR or Maxwell).