From Scaling to String Theory:

Changing Styles of Discovery in Fundamental Physics

Curtis CallanPhysics DepartmentPrinceton University

Recollection and Reflection

• Some 30 years ago I had the good luck to be involved in work which led to the establishment of the theory of the strong interactions.

• This episode was a “normal” revolution in fundamental physics: experimental discovery stimulating (mild) theoretical innovation

• Since then, the frontier of fundamental theory has moved on to deeper and harder questions (grand unification, quantum gravity,..)

• Much has changed – to the point that some observers say that what much of the theory community does (string theory) isn’t physics!

• Since I’ve been actively involved in the enterprise during this whole period, I thought I would review and compare fundamental physics then (scaling) and fundamental physics now (string theory).

• It is very definitely not a case of “plus ca change, plus c’est la meme chose”: our science has gone through a very major sea change.

Strong Interaction Theory: Historical Context• Yukawa – QFT of mesons and nucleons; inspired QED analog• QFT is conceptual key – dynamics of point entities (with only mass, spin as

attributes) marrying QM and relativity• Divergences were a problem but, by the 50s, renormalization was

understood and QED gave amazing agreement with experiment.• In the 60s, the explosive growth of the “zoo” of excited states of the

nucleon and the pion seriously confused things:– Clearly, it couldn’t be “one particle, one field” … but what was it?

• This situation led to two competing ideologies:Rejectionist: Drop QFT as the dynamical framework and invent somethingCompletely new to capture hadron complexity “naturally”.

Loyalist: Keep QFT, but find principles to pick the right fields/Lagrangian. Strongly motivated by symmetries, esp. spontaneously broken chiral, which were readily derivable from QFT. Strongly driven by the success of SU(3), PCAC, soft-pion theorems.

• Fields: (electron) & A (photon)

• Lagrangian:

• Propagators and interactions:

• Rules for Feynman diagrams for processes:

( g )electron = 2 + + … (accurate to 10th digit!)

• QED has parameters (me and ), and no way of “explaining” them

QED: The First Fundamental QFT

Deep Inelastic Electroproduction• To see inside a QFT, you need access to the operators of the theory. The currents of QED

and the weak intn’s were only option.• Inclusive electroproduction on nucleons (SLAC ~ ’69) was ideal:

• Measuring total cross-sections summed over X (as fn of E,E’,) one extracts

• High-energy limit ~ operators close to each other in spacetime ~ direct view of what’s inside the nucleon. Expectations for the outcome were mixed ..

EE’

How the experiments are done

• SLAC data showed striking high-energy behavior: in the limit q2 → -∞ with x = - q2/held fixed, the structure functions F1 = W1 and F2 = W1 “scale” by becoming functions of x only (Bjorken): Fi → Fi (x) .

• Interpreted by viewing the nucleon (in the light-come frame) as a bag of “free” point constituents, each carrying a fraction x of total momentum P:

• Heuristic argument automatically gave Bjorken scaling to the structure functions. Assumptions about “parton” charges/spins led to sum rules that could in principle discriminate different options.

• The real question was whether the partons were the fundamental fields of the QFT of the strong interactions … if so, shouldn’t you get these results directly from QFT dynamics …. predict Pa(x) etc.?

Discovering and Interpreting Scaling

Pa(x) is probability of finding type a parton with momentum fraction x, charge Qa in target

• Wilson’s Operator Product Expansion gave a different heuristic:

• Dimension is associated with scale invariance, a broken symmetry recovered at short distance .. but perhaps with non-canonical dimension values.

• Elaborate analysis needed to connect all this with the deep inelastic story

• We can now see that Bjorken scaling requires that the anomalous dimension vanish for this infinite set of composite operators. How?

First Steps Toward Scaling in QFT

On are local operators, dJ are operator dimns, the Cn are expansion coeffs.

Scaling in Generic QFT: C-S Equation• Attention now focused on scale invariance as a symmetry: what is its status

in QFT? Can it become exact at high energy?• Symmetries can be broken explicitly, but also by quantum anomalies (as in

the Adler-Bell-Jackiw anomaly for chiral invariance). • For scale invariance, this logic led to the “Callan-Symanzik” equations, which

imply a universal flow equation for OPE coefficients On:

• Solution of this characteristic eqn. trades c.c. flow for energy increase:

• Applied to electroproduction, we get Wilson (not Bjorken) scaling:

Renormalization scale Anomalous dimension Coupling flow function

Scaling Reconciled with QFT: Asymptotic Freedom• Electroproduction scaling governed by anomalous dimensions of a special

series of operators (lowest dimension for spin n ):

• Only plausible mechanism is zero-coupling fixed point: gf = 0 ! But even then you don’t quite get Bj scaling … there are log corrections to scaling, driven by details of expansion around g = 0:

• Problem is to find specific QFT with gf = 0,which is to say with negative one-loop !

• Dramatic GWP ‘73 discovery that only non-abelian gauge theories have right -function sign uniquely identified strong interaction QFT.

Modern Experimental Results For Deep Inelastic Electron Scattering

Note that, at moderate values of x, the structure function F2 (x,Q2) is nearly independent of Q2. This was the original SLAC “scaling” discovery.

The slow variation with Q2 caused by asymptotic freedom could only be seen in very high-energy experiments which took years to do (DESY/HERA)

The observed slow variation of F2 (x,Q2) with Q2 follows the specific predictions for QCD with SU(3) gluons, on the nose!

QCD: The New QED• Consistency with Bjorken scaling (modulo logs) & some basic facts about hadron physics

leads to quarks glued by SU(3)color gauge bosons

• Much like QED, except that the constituents have never been seen directly. Confinement: believable but, to this day, unproven.

• Predict specific scaling violations with an intricate dependence on gauge group and “partial wave”. Infinite number of rigorous predictions about large q2 behavior of F2(x,q2). Agreement with experiment is now amazing.

• Nothing else can be predicted from first principles! Especially not the spectrum of hadron states, the original motivation for colored quarks. Amazing luck that we were able to sidestep the strong coupling problem for one observable!

• But there is NO DOUBT that we have found the true QFT explanation of the strong interactions. Experiment provided broad hints, not direct revelation.

• Classic example of a conservative revolution in science with experiment and theory working together in a classic push-pull partnership.

Beyond Asymptotic Freedom

• Standard Model (conservative revolution within QFT)– Successful search for QFT foundation of strong interactions was paralleled by similar

development in electroweak theory: weak and em forces were unified in a (spontaneously broken) SU2xU1 gauge theory.

– Big difference was the symmetry breaking and the QED-like ability to accurately calculate real physical quantities

– Upshot is QFT Standard Model of all physics below the EWSB scale.

• String Theory (radical rejection of the QFT dynamical framework) – Motivated by strong interaction zoo, reject QFT and invent new dynamics that captures

hadron spectrum. This development was sideswiped by QCD!– Beautiful invention: unique extension of dynamics of points to dynamics of lines.

Captures something like a hadron spectrum w/out constituents– But: it only works in 10D spacetime, requires superpartners, has mass-less spin 2 particle

…. It turned out to be a finite theory of quantum gravity, not a theory of hadrons!– Serendipity strikes again: whole new theoretical playground with no compelling

experimental motivation. Theorists responded to it as cats to catnip!

In 1970’s two fundamental theory trends took shape:

More History (the 80s)• Both tracks flourished, but diverged in style and content• Standard Model :

– Experiment near the EW symmetry-breaking scale verifies QFT pre-dictions with astounding accuracy. No hint of “beyond SM” physics.

– Deep questions (how many generations? what are the mq?) are answered, numerically, not deeply.

– Fruitful experiment/theory interaction, but no real surprises• String Theory:

– Heterotic string brings SM chiral fermions into same framework as gravity.– Modern version of Kaluza-Klein shows how to reduce 10D theory to 4D with the help of

special 6D string-compatible spaces (Calabi-Yau)– Modern math (topology and algebraic geometry) brought into play and physics questions

(how many generations?) turned into mathematics.– Initial hope for deriving THE Standard Model from first principles faded with the discovery of

a vast multiplicity of possible Calabi-Yau spaces• Intellectual need for coherent “beyond SM” framework was met but, despite much theoretical

ingenuity, a clear match between new theory and old exp’t did not emerge.

Yet More History (the 90s)• Standard Model: Second decimal place refinement of results

– The flow of experimental results decreased somewhat– The top quark is found at an unexpectedly large mass. The Higgs meson continues to

hide, even as experiment pushes to higher mass– No evidence of “beyond SM” physics found, even in very sensitive rare decay searches

… except for the discovery of neutrino oscillations!• String Theory : Learns how to deal with non-perturbative physics

– Duality (g to 1/g) between different string theories is discovered– It appears that apparently different string theories are simply different

compactifications of a new D=11 (not 10!) supergravity.– String solitons (D-branes) are found and put on a solid dynamical footing …

• Shift of Focus: Understand the non-perturbative dynamics of string theory for its own sake, without worrying about direct contact with experiment.

– This has positive outcomes (discovery of the gauge/string duality) – On the negative side, the intellectual and personnel overlap between the two schools of

fundamental physics reaches a new low.

“Physics in Crisis”

• Physics has lost focus as a field (and appeal to students & funders). Why?– Then : Pre-eminence of particle physics meant consensus that physics is about

finding the laws of Nature. Clear value hierarchy.– Now : Decline (relative) of particle physics has eroded goals/mission consensus– This “Fall of Berlin Wall” has led to squabbles between subdisciplines, between

big & small science, between basic & applied … to intellectual Balkanization.– Nagel claims that there is an undercurrent: many no longer accept that

reductionism is superior science and the primary mission of physics.– All of the above is bad for morale, funding, attracting students, etc.

• Nagel’s suggested remedy: more active talk between the subdisciplines, attempt to find common “big” questions to address, …..

– Even if you don’t fully accept his argument, his challenge is particularly relevant to the current state of string theory ..

• Is Nagel right, even partially, and how should we respond?

In a Physics Today article, Sid Nagel made the following provocative claims:

String Theory ≠ Science As Usual • It is in the great reductionist tradition: find the deepest/simplest laws,

encompass the most phenomena, reduce complexity to simplicity.• Previous reductionist “events” were in response to new phenomena.

However, no specific observation points directly to string theory. • Compelling arguments for strings are mainly theoretical (taming of gravity

divergences, rationale for supersymmetry, ..). – But a clear mathematical formulation of the theory, such as we have for QCD,

still eludes us: the string field theory quantum path integral is not yet well-defined .. it may need 25th century mathematics to master it.

• The scale jump between the “old regime” (Standard Model, 103 GeV) and the new (Planck scale, 1019 GeV) is of unprecedented size. Do we really expect pure thought to take us so far?

• String theory has morphed into a subject that is more like math than physics (some folks say): its priorities are no longer set by physics issues.

• Despite all these complaints, some of the best talent goes into this strange field …. it must be doing something right!

String Theory is Alive and Well• Quantum dynamics at high energy must run into quantum gravity – but all

attempts at point particle QFT of gravity have failed (non-renormalizable)• String theory is the only dynamical framework that meets this challenge. It is

also the most natural generalization of point particle dynamics.• It works because it is “non-local” and has a fundamental length. Putting such

features into a QFT causes disaster. String theory seems to be unique.• The formal structure (string field theory, for instance) is starting to fall into

place, so there is some hope of achieveing a clean axiomatic formulation.• The scale gap between “old” and “new” physics is very alarming, but this

may simply be the price we pay for having asymptotic freedom … logarithms of energy have to get big to change the nature of the game.

• In the end, we pursue because this is where the progress of science has led us …. and because conceptual progress continues unabated.

Huge Impact on Other Fields

• Conformal Field Theory in 2D – Basic dynamics of the string worldsheet. Exact solutions of 2D CFT are often

interpretable as string-compatible spacetimes .. And critical pts of CM systems• String Solitons (D-branes etc.)

– Extended objects of various dimensions exist and can be mixed and matched to create complex string theory spacetimes

– Major consequence – resolution of the black hole entropy problem of classical GR. Multiple ways of combining solitons to get same mass/charge … entropy.

• Gauge/String Duality (AdS/CFT)– Totally new perspective on ordinary QFT! String theory in special 10D

background is identical to a QCD-like theory in 4D. Gravity w/out gravity!– Duality means that a strong-coupling limit of gauge theory is a weak-coupling

limit of gravity/string theory.– Completely new ways of attacking “ordinary” strong coupling problems

The dynamical structures of string theory have many unexpected uses:

External Impact (cont.)• Symbiosis with Modern Mathematics

– String theory makes maximal use of modern algebraic geometry (viz. Calabi-Yau manifolds for compactification) and has stimulated cross-field interaction.

– It has also brought new ideas to mathematics: viz. “mirror manifolds” of different classical topology that smoothly connect under string dynamics.

• Fertilization of Cosmological Thinking– Inflationary cosmology must come to grips with the initial singularity – if only

to understand the fluctuation spectrum. This question can only be posed at the string scale and only string theory can hope to be a quantum theory of the universe.

– String theorists are just now grappling with time-varying geometries and spacelike singularities. Cosmologists are allowing themselves to think about “string-inspired” dynamical options for the Big Bang.

• String theory has a mathematical and physical richness which vastly exceeds its original scope and just continues to grow .. you can’t ignore it.

Final Thoughts• String theory is a strange beast, quite unlike the fundamental theories whose

discovery is recounted in the textbooks.• String theory is working (slowly, to be sure) toward its own ends … one should be

patient and remember how long it took for QFT to become a respectable and fully functional framework for physical thought.

– As a side benefit, it is invigorating and inspiring other parts of physics and even mathematics.

• I would argue that this is all very good for SCIENCE:– People inside and outside of science are excited by the knowledge that big questions

of fundamental import are on the agenda• I believe that, without a healthy fundamental science, the rest of science cannot

prosper. Its getting harder and harder, but we can’t give up yet!– String theory is the physics flag-bearer in this regard: it tackles the most challenging

BIG QUESTIONS (the nature or spacetime …)– Its answers are non-intuitive; its amazing that they can be addressed at all.

• The ultimate indicator of health is the continued flow of super-talented young people into the field … which continues without check.