Abstract
Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here (along with a review of string theory for philosophers of physics). Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of view it plays only a formal role in the explanation.
Highlights
The goal of this paper is to explain the significance of the conformal symmetry of string theory
Let us suppose that it is ‘closed’, meaning that its ends are joined into a loop
There are two claims involved in the view that background fields represent coherent states: (i) that the string is an adequate ‘theory of everything’, in the sense that the string spectrum includes quanta for all desired background fields and (ii) that the terms in the action accurately capture the effective behavior of those coherent states
Summary
The goal of this paper is to explain the significance of the conformal symmetry of string theory. Along the way we will introduce the basics of string theory in a streamlined fashion, drawing on familiar ideas from classical and quantum field theory. We will explain how general relativity is a ‘consequence’ of string theory: not merely in the sense that it contains massless spin-2 particles – gravitons – but in the very strong sense that the coherent states of the graviton obey the Einstein field equations – gravitons truly form the gravitational field. This result follows from reimposing conformal symmetry in quantized string theory; so in the final section of the paper we sketch some more esoteric considerations justifying this assumption
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