Titlebook: String Field Theory; A Modern Introductio Harold Erbin Textbook 2021 Springer Nature Switzerland AG 2021 String scattering amplitudes.Off-s

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Worldsheet Path Integral: Complex Coordinates metric. In this chapter, we start to use complex coordinates and finally take the background metric to be flat. This is the usual starting point for computing amplitudes since it allows to make contact with CFTs and to employ tools from complex analysis. We first recall few facts on 2. complex mani

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Conformal Field Theory on the Planeeometry of the sphere and the relation to the complex plane and to the cylinder, in order to make contact with the string worldsheet. Then, we discuss classical CFTs and the Witt algebra obtained by classifying the conformal isometries of the complex plane. Then, we describe quantum CFTs and introdu

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BRST Quantizatione. One can then use all the CFT techniques to extract information on the spectrum, which makes this approach more powerful. Moreover, this also provides an elegant description of states and string fields. In this chapter, we set the stage of the BRST quantization using the CFT language, and we apply

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String Fieldsibilities for describing it. We will see that the string field is a functional and, for this reason, it is more convenient to work with the associated ket field, which can itself be represented in momentum space. We focus on what to expect from a free field, taking inspiration from the worldsheet t

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Free BRST String Field Theorytroduce some general tools and structures in a simpler setting. Moreover, the free SFT is easily constructed and does not require as much input as the interactions. In this chapter, we discuss mostly the open string, keeping the closed string for the last section. We start by describing the classica

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Introduction to Off-Shell String Theoryar, local coordinates and factorization—by focusing on the 3- and 4-point amplitudes. We then prepare the stage for a general description of off-shell amplitudes. We focus again on the closed bosonic string only.

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Geometry of Moduli Spaces and Riemann Surfacesrevious chapter. Then, we can characterize the tangent space that we will need in the next chapter to write the .-forms on . necessary to write the amplitudes. Finally, we introduce the notion of plumbing fixture, an operation that glues together punctures located on the same or different surfaces.