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

https://arxiv.org/pdf/hep-th/9411028v1.pdf

What is string theory

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

Vesicles consisting of a bilayer membrane of amphiphilic lipid molecules are remarkably flexible surfaces that show an amazing variety of shapes of different symmetry and topology. Owing to the fluidity of the membrane, shape transitions such as budding can be induced by temperature changes or the action of optical tweezers. Thermally excited shape fluctuations are both strong and slow enough to be visible by video microscopy. Depending on the physical conditions, vesicles adhere to and unbind from each other or a substrate. This article describes the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations. The preferred shapes arise from a competition between curvature energy, which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect. These shapes of lowest energy are arranged into phase diagrams, which separate regi...

Configurations of fluid membranes and vesicles

We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.

http://math.univ-lyon1.fr/~attal/Okounkov/okounkov-nekrasov

Seiberg-Witten theory and random partitions

Critical properties of randomly triangulated planar random surfaces

Analytical and numerical study of a model of dynamically triangulated random surfaces

A matrix model for the two-dimensional black hole

We construct and study a matrix model that describes two dimensional string theory in the Euclidean black hole background. A conjecture of V. Fateev, A. and Al. Zamolodchikov, relating the black hole background to condensation of vortices (winding modes around Euclidean time) plays an important role in the construction. We use the matrix model to study quantum corrections to the thermodynamics of two dimensional black holes.

A Matrix Model for the Two Dimensional Black Hole

The O(n) model on a two-dimensional dynamical random lattice is reformulated as a random matrix problem. The critical properties of the model are encoded in the spectral density of the random matrix which satisfies an integral equation with Cauchy kernel. The analysis of its singularities shows that the model can be critical for −2 ≤ n ≤ 2 and allows the determination of the anomalous dimensions of an infinite series of magnetic operators. The results coincide with those found in Ref. 11 for 2d quantum gravity.

Ivan K. Kostov

Papers

Critical properties of randomly triangulated planar random surfaces

Analytical and numerical study of a model of dynamically triangulated random surfaces

A matrix model for the two-dimensional black hole

A Matrix Model for the Two Dimensional Black Hole

O($n$) Vector Model on a Planar Random Lattice: Spectrum of Anomalous Dimensions