Why strings?


String theory has a bizarre intellectual history. It originated in the late 60's, as an attempt to understand the properties of certain strongly-interacting particles known as mesons. It was observed experimentally that mesons could be grouped into families. Members of the same family had similar properties, aside from ever-increasing masses and spins. To a good approximation a linear relationship was found between the meson spins J and their squared masses m2 .

Mass-spin relationship for mesons, from [1].

String theory originated as an attempt to explain this relationship, which is usually expressed in the form

The picture was that a meson consisted of two particles (`quarks') tied together by a piece of `string' - think of two golf balls connected by an elastic band. If the system spins around the quarks will want to fly apart. This generates a centrifugal force that pulls on the string. The bigger the spin, the more the string gets stretched, and this turns out to increase the mass of the meson exactly according to the above formula.

A meson according to string theory.

Although it had some of the right properties, ultimately string theory failed as a theory of strong interactions. It was replaced with a theory known as QCD (for `quantum chromodynamics'). QCD is a gauge theory, as is ordinary electromagnetism. In QCD one regards a meson as made up of two quarks which interact via a type of electric field. In QCD, unlike ordinary electromagnetism, electric flux lines attract each other, and tend to bunch together. These bunched-together flux lines behave like a piece of string. In this way QCD predicts the correct linear relationship between meson masses and spins, as well as accounting for many other observed properties of strong interactions.

A picture of flux lines in QED (left) and QCD (right).

Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

The vibrational state of a string that corresponds to a graviton.

No one has really been able to make sense of strings moving around in four dimensions. But strings moving in ten dimensions (with lots of supersymmetry) have all sorts of amazing properties. In ten dimensions a systematic mathematical analysis becomes possible, and remarkably all the ingredients needed to describe nature - gauge fields and chiral fermions, as well as gravity - are found to arise as different vibrational states of the string. These days ten dimensional string theory is the best candidate for unifying gravity with all the other particles and forces observed in nature.

So was it just an accident that string theory and QCD had some properties in common, such as the linear mass-spin relationship for mesons? The answer, it turns out, is no. Very strong arguments have been put forward that a certain ten dimensional string theory (`IIB on AdS5xS5') is completely equivalent to a four dimensional gauge theory (`N=4 super Yang-Mills') [2]. The gauge theory in question is not QCD, although it's closely related. For example, the force between two quarks can be calculated in the gauge theory, by studying the behavior of the electric field in four dimensions. The force can also be calculated in the string theory, by studying a string which connects the two quarks. Remarkably, even though the string can move around in all ten dimensions, while the electric field can only spread out in four dimensions, the two forces exactly agree [3].

The interaction between two quarks according to IIB string theory (left) and gauge theory (right).

This sort of relation, between string theory and gauge theory, has been the focus of my research over the past few years. There are many puzzles to be sorted out. The problem is that at first sight the gauge theory doesn't have anything to do with gravity: gravity is encoded in the gauge theory in a very subtle way. I've worked on understanding how ten dimensional `causal structure' (the property that objects always travel slower than the speed of light) emerges from the gauge theory [4]. I've also worked on understanding the horizon of a black hole from the gauge theory point of view [5]. The main obstacle to making further progress along these lines is that the gauge theory is quite difficult to solve mathematically. A group of us have developed a set of approximations to help in studying the gauge theory [6]. Using these approximations we've been able to count the states of a ten dimensional black hole by performing a gauge theory calculation [7], and we've studied the dynamics of a test particle moving near a black hole [8]. This line of research ultimately led to a simple description of black holes, in terms of gauge-theory-like degrees of freedom that can be thought of as living on the event horizon [9,10]. More recently I've been investigating the description of local bulk operators in this sort of gravity / gauge theory correspondence [11].

I've also gotten interested in applications of string theory to cosmology. Several of us have been investigating the cosmological implications of having extended objects present in the very early universe [12,13,14].


References:

[1] Systematics of q anti-q states in the (n,M2) and (J,M2) planes
A. Anisovich, V. Anisovich and A. Sarantsev, hep-ph/0003113
[2] The large N limit of superconformal field theories and supergravity
Juan Maldacena, hep-th/9711200
[3] Wilson loops in large N field theories
Juan Maldacena, hep-th/9803002
[4] Gauge theory origins of supergravity causal structure
Daniel Kabat and Gilad Lifschytz, hep-th/9902073
[5] Tachyons and black hole horizons in gauge theory
Daniel Kabat and Gilad Lifschytz, hep-th/9806214
[6] Approximations for strongly-coupled supersymmetric quantum mechanics
Daniel Kabat and Gilad Lifschytz, hep-th/9910001
[7] Black hole entropy from non-perturbative gauge theory
Daniel Kabat, Gilad Lifschytz and David Lowe, hep-th/0105171
[8] Probing black holes in non-perturbative gauge theory
Norihiro Iizuka, Daniel Kabat, Gilad Lifschytz and David Lowe, hep-th/0108006
[9] Quasiparticle picture of black holes and the entropy-area relation
Norihiro Iizuka, Daniel Kabat, Gilad Lifschytz and David Lowe, hep-th/0212246
[10] Stretched horizons, quasiparticles and quasinormal modes
Norihiro Iizuka, Daniel Kabat, Gilad Lifschytz and David Lowe, hep-th/0306209
[11] Local bulk operators in the AdS/CFT correspondence
Alex Hamilton, Daniel Kabat, Gilad Lifschytz and David Lowe, hep-th/0506118 and hep-th/0606141
[12] Brane gas cosmology in M-theory: late time behavior
Richard Easther, Brian Greene, Mark Jackson and Daniel Kabat, hep-th/0211124
[13] Brane gases in the early universe: thermodynamics and cosmology
Richard Easther, Brian Greene, Mark Jackson and Daniel Kabat, hep-th/0307233
[14] String windings in the early universe
Richard Easther, Brian Greene, Mark Jackson and Daniel Kabat, hep-th/0409121