Lectures notes on string theory sorbonneuniversite. Now lets do special relativity using this notation. It will be expressed as the invariant length of the worldline s z. The starting point for string theory is the idea that the pointlike particles of particle physics can also be modeled as onedimensional objects called strings. Introduction to string theory heidelberg university.
String theory in a curved space is a consistent quantum theory if the quantum nonlinear twodimensional sigma model 1, 2 is conformally invariant. So, without fermions and supersymmetry, string theory is consistent in 26 spacetime dimensions. And that is the equation of distances in euclidean three space in tensor notation. Conformal field theory for string theorists christopher p. The metric on the target space obeys the einstein equations.
We are thus led to the following general definition of perturbative string theory. General relativitymetric tensor wikibooks, open books for. If we write h for the 1 1 metric tensor of, and g for the d d metric tensor of spacetime. Lectures on string theory uci physics and astronomy. Introduction to string theory institut fur theoretische physik. Note that the dual relation to open string theory is not required for this conclusion. It is clear that a nontrivial ky tensor can square to the metric as long as c 2. String theory is a theoretical framework that attempts to address these questions and many others. Yang institute for theoretical physics, department of physics and astronomy stony brook university, stony brook, ny 11794 abstract a write up of about ten lectures on the adscft correspondence given as part of a second semester course on string theory. A manifold equipped with a positivedefinite metric tensor is known as a riemannian manifold. The result is therefore an n 4 u2 gauge theory on the. The second approach, however, is not tied to perturbation theory or.
This set of notes is based on the course introduction to string theory which was taught by prof. Metric tensor and the line element phys 500 southern illinois university september 22, 2016 phys 500 southern illinois university metric tensor and the line element september 22, 2016 1 16. In preparing this two volume work our intention is to present to engineering and science students a modern introduction to vectors and tensors. The minus sign in the square root reflects our choice of metric, namely. These strings come in open free endpoints and closed connected endpoints varieties. For example, in the newtonian theory of gravity the gravitational force depends only on the current distance between two interacting bodies. Feynman diagrams in string theory edward witten pitp, july 25, 20. String theory is a quantum theory of 1d objects called strings. Consequently, there are no local degrees of freedom in topological string theory. Our notation will not distinguish a 2,0 tensor t from a 2,1 tensor t, although a notational distinction could be made by placing marrows and ntildes over the symbol, or by appropriate use of dummy indices wald 1984. What every physicist should know about string theory some of natures rhymesthe appearance of similar structures in different areas of physicsunderlie the way that string theory potentially unifies gravity with the other forces of nature and eliminates the ultraviolet divergences that plague quantum gravity.
Show that the nambugoto and polyakov expressions for the relativistic string are classically equivalent. Pdf it is shown that the equation of motion for a nambu string in curved space can be. Introduction to string theory chapter 0 eth zurich, hs prof. Along the way we will introduce the basics of string theory in a streamlined fashion. Pdf poissonlie uduality in exceptional field theory. If one adds fermions, one only needs 10 dimensions, as mentioned earlier. Introduction to string theory universiteit utrecht.
This, not coincidentally, is the subject of the new book. As shown earlier, in euclidean 3space, is simply the kronecker delta matrix. Which opinion one prefers is of course a matter of taste, but it is a fact that all three of. What every physicist should know about string theory. We may play this game in the euclidean space en with its \dot inner product. Through integration, the metric tensor allows one to define and compute the length of curves on the manifold. Classical and quantum gravity the cotton tensor in riemannian spacetimes to cite this article. Metric tensor in special and general relativity physics. So if one body changes its position then the other one \feels this immediately, no matter how great the distance between them is. An introduction to string theory kevin wray abstract. However, a look at the standard string theory reveals a serious di. What ive understood so far has come from my course lecture notes used in conjunction with the road to reality by roger p. String theory and the geometry of the universes hidden.
It combines many interesting topics of quantum eld theory in two and higher dimensions. If we succeed, the right hand side of the loop equation will arise from the degenerate metrics. Sl2, bbb z tensionless string backgrounds in iib string theory. What distinguishes it from other approaches to quantising gravity is that string theory is currently the only theory that is able to provide a uni ed. Pdf derivation of the string equation of motion in general relativity. The presence of twodimensional diffeomorphism invariance in string theory leads to the condition that c 26.
String theory describes how strings propagate through space and interact with each other. The operation is fully analogous to the construction of topological field theory which is a related concept. The antisymmetric tensor field is derived in the context of general relativity with. The polyakov action has reparameterisation and weyl invariance, yet the nambugoto action only has reparametrisation.
We have also drawn on some ideas from the books string theory and. A mathematical derivation of the east tennessee state. Emergent spacetime in string theory by tiziana vistarini thesis. A metric tensor is called positivedefinite if it assigns a positive value gv, v 0 to every nonzero vector v. Im having trouble understanding the metric tensor in general relativity. Example sheet 1 corrections and suggestions should be emailed to r. So, the first great achievement of string theory was to give a consistent theory of quantum gravity, which resembles gr at macroscopic distances. Topological string theory is obtained by a topological twist of the worldsheet description of ordinary string theory. You cant walk across a room without using a tensor the pressure tensor. The spacetime string energymomentum tensor follows as usual by taking the functional derivative of the action 2. At this point if we were going to discuss general relativity we would have to learn what a manifold 16.
Introduction to tensor calculus for general relativity. The relevant mass less n 4 4 supermultiplets are the supergravity multiplet and the vector multiplet. Pdf poissonlie duality provides an algebraic extension of conventional abelian and nonabelian target space dualities of string theory and has seen. String theory for idealists string theory is the leading proposal for a fundamental uni ed theory of quantum gravity and quantum field theory. This is a set of latexed notes on string theory from liam mcallisters physics 7683. A string is a special case of a pbrane, where a pbrane is a pdimensional object moving through a dd. The supergravity multiplet contains the metric, six vectors the graviphotons, a scalar and an antisymmetric tensor, as well as four majorana gravitini and four majorana spin.
A di erent metric will, in general, identify an f 2v with a completely di erent ef 2v. Literature this is the writeup of my course introduction to string theory, held in the master programme at the university of heidelberg during winter term 201112. It is called the metric tensor because it defines the way length is measured. The scalar product is a tensor of rank 1,1, which we will denote i and call the identity tensor. You cant align the wheels on your car without using a tensor the inertia tensor. Introduction the goal of this paper is to explain the signi cance of the conformal symmetry of string theory. Scalar products of tangent vectors, using minkowski metric. A mathematical derivation of the general relativistic schwarzschild metric an honors thesis presented to the faculty of the departments of physics and mathematics east tennessee state university in partial ful.