What is String Theory?

TL;DR

The paper surveys how conformal field theory underpins string perturbation theory and how BRST quantization, together with worldsheet conformal invariance, yields a consistent framework for string dynamics and spacetime physics. It then surveys dualities, background independence, and the role of sigma-models in encoding spacetime backgrounds, with detailed attention to circle compactification, T- and S-dualities, and the emergence of gauge symmetries. A substantial portion is devoted to nonperturbative formulations, including string field theory and matrix models, especially in the solvable D=2 (c=1) setup, where gravity and tachyon dynamics are tractable and illuminate how strings may be collective excitations of simpler degrees of freedom. The work emphasizes that different apparent string theories are often different vacua or dual descriptions within a single underlying theory, and highlights the profound implications of modular invariance, OPE associativity, and BRST cohomology for the nonperturbative structure of string theory.

Abstract

The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and Dualities 4. String Field Theory or Not String Field Theory 5. Matrix Models

Figures (30)

• Figure 1: a) Contours centered on $z=0$. b) For given $z_2$ on contour $C_2$, contour $C_1 - C_3$ is contracted.
• Figure 2: a) World-sheet (shaded) with state $| \psi_{\cal A} \rangle$ on the boundary circle, acted upon by $Q$. b) Equivalent picture: the unit disk with operator ${\cal A}$ has been sewn in along the dotted line, and $Q$ contracted around the operator.
• Figure 3: a) World-sheet with two local operators. b) Integration over fields on the interior of the disk produces boundary state $| \psi_{ij,z,\bar{z}} \rangle$. c) Sewing in a disk with the corresponding local operator. Expanding in operators of definite weight gives the OPE.
• Figure 4: Schematic picture of OPE associativity.
• Figure 5: The torus by periodic identification of the complex plane. Points identified with the origin are indicated. Edges $a$ and $a'$ are identified, as are edges $b$ and $b'$.