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Introduction

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String Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 980))

Abstract

In this chapter, we introduce the main motivations for studying string theory, and why it is important to design a string field theory. After describing the central features of string theory, we describe the most important concepts of the worldsheet formulation. Then, we explain the reasons leading to string field theory (SFT) and outline the ideas which will be discussed in the rest of the book.

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Notes

  1. 1.

    There are also indications that a theory of membranes (2-branes) in 10 + 1 dimensions, called M-theory, should exist. No direct and satisfactory description of the latter has been found and we will thus focus on string theory in this book.

  2. 2.

    Entering in the details would take us too far away from the main topic of this book. Some of the problems found when dealing with (p > 2)-branes are: how to define a Wick rotation for 3-manifolds, the presence of Lorentz anomalies in target spacetime, problems with the spectrum, lack of renormalizability, impossibility to gauge-fix the worldvolume metric [1,2,3,4,5,6,7, 13, 16,17,18, 44, 58, 61,62,63, 71, 78].

  3. 3.

    We focus mainly on the bosonic string theory, leaving aside the superstring, except when differences are important.

  4. 4.

    In the introduction, we set α′ = 1.

  5. 5.

    These conditions exclude the cases of free theories and higher-spin theories.

  6. 6.

    The case N L < N R is identical up to exchange of the left- and right-moving sectors.

  7. 7.

    We ignore unoriented strings in this discussion. The associated worldsheets can have cross-caps which make the surfaces non-orientables.

  8. 8.

    For simplicity we focus on closed string amplitudes in this section.

  9. 9.

    There is a caveat to this statement: UV divergences reappear in string field theory in Lorentzian signature due to the way the theory is formulated. The solution requires a generalization of the Wick rotation.

    Moreover, this does not hold for open strings whose moduli spaces contain those regions: in this case, the divergences are reinterpreted in terms of closed strings propagating.

  10. 10.

    Such spurious singularities are also found in supergravity.

  11. 11.

    The on-shell condition is a consequence of the BRST and conformal invariance. While the first will be given up, the second will be maintained to facilitate the computations.

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  1. Center for Theoretical Physics Massachusetts Institute of Technology, Cambridge, MA, USA

    Harold Erbin

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Erbin, H. (2021). Introduction. In: String Field Theory. Lecture Notes in Physics, vol 980. Springer, Cham. https://doi.org/10.1007/978-3-030-65321-7_1

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