17
Superstring
Abstract
Superstring theory is generally the starting point for physical model building.
It has indeed several advantages over the bosonic string, most importantly, the
removal of the tachyon and the inclusion of fermions in the spectrum. The goal
of this chapter is to introduce the most important concepts needed to generalize
the bosonic string to the superstring, both for off-shell amplitudes and string field
theory. We refer to the review [2] for more details.
17.1 Worldsheet Superstring Theory
There are five different superstring theories with spacetime supersymmetry: the
types I, IIA and IIB, and the E 8 × E 8 and SO(32) heterotic models.
In the Ramond–Neveu–Schwarz formalism (RNS), the left- and right-moving
sectors of the superstring worldsheet are described by a two-dimensional superconformal field theory (SCFT), possibly with different numbers of supersymmetries.
The prototypical example is the heterotic string with N = (1, 0), and we will
focus on this case: only the left-moving sector is supersymmetric, while the rightmoving is given by the same bosonic theory as in the other chapters. Up to minor
modifications, the type II theory follows by duplicating the formulas of the leftmoving sector to the right-moving one.
17.1.1 Heterotic Worldsheet
The ghost super-CFT is characterized by anti-commuting ghosts (b, c) (left-moving)
and ( ¯
b, ¯
c) (right-moving) with central charge c = (−26, −26), associated to
diffeomorphisms, and by commuting ghosts (β, γ ) with central charge c = (11, 0),
associated to local supersymmetry. As a consequence, the matter SCFT must have a
© Springer Nature Switzerland AG 2021
H. Erbin, String Field Theory, Lecture Notes in Physics 980,
https://doi.org/10.1007/978-3-030-65321-7_17
339
Superstring
Abstract
Superstring theory is generally the starting point for physical model building.
It has indeed several advantages over the bosonic string, most importantly, the
removal of the tachyon and the inclusion of fermions in the spectrum. The goal
of this chapter is to introduce the most important concepts needed to generalize
the bosonic string to the superstring, both for off-shell amplitudes and string field
theory. We refer to the review [2] for more details.
17.1 Worldsheet Superstring Theory
There are five different superstring theories with spacetime supersymmetry: the
types I, IIA and IIB, and the E 8 × E 8 and SO(32) heterotic models.
In the Ramond–Neveu–Schwarz formalism (RNS), the left- and right-moving
sectors of the superstring worldsheet are described by a two-dimensional superconformal field theory (SCFT), possibly with different numbers of supersymmetries.
The prototypical example is the heterotic string with N = (1, 0), and we will
focus on this case: only the left-moving sector is supersymmetric, while the rightmoving is given by the same bosonic theory as in the other chapters. Up to minor
modifications, the type II theory follows by duplicating the formulas of the leftmoving sector to the right-moving one.
17.1.1 Heterotic Worldsheet
The ghost super-CFT is characterized by anti-commuting ghosts (b, c) (left-moving)
and ( ¯
b, ¯
c) (right-moving) with central charge c = (−26, −26), associated to
diffeomorphisms, and by commuting ghosts (β, γ ) with central charge c = (11, 0),
associated to local supersymmetry. As a consequence, the matter SCFT must have a
© Springer Nature Switzerland AG 2021
H. Erbin, String Field Theory, Lecture Notes in Physics 980,
https://doi.org/10.1007/978-3-030-65321-7_17
339