A
Conventions
This book uses natural units where c = ¯
h = 1, but the string length s (or Regge
slope α ) is kept.
A bar is used to denote both the complex conjugation and the anti-holomorphic
operators. The symbol := (resp,. =:) means that the LHS (RHS) is defined by the
expression in the RHS (LHS).
A.1
Coordinates
The number of spacetime (target-space) dimensions is denoted by D = d +1, where
d is the number of spatial dimensions. The corresponding spacetime and spatial
coordinates are written with Greek and Latin indices:
x
μ
= (x
0 , x
i ),
μ = 0, . . . , D − 1 = d
i = 1, . . . , d.
(A.1)
When time is singled out, one writes x 0 = t in Lorentzian signature and x 0 = t E
in Euclidean signature (or x 0 = τ when there is no ambiguity with the worldsheet
time).
A p-brane is a (p + 1)-dimensional object whose worldvolume is parametrized
by coordinates:
σ
a
= (σ
0 , σ
α ),
a = 0, . . . , p − 1,
α = 1, . . . , p.
(A.2)
The time coordinate can also be singled out as σ 0 = τ M in Lorentzian signature and
σ 0 = τ in Euclidean signature. For the string, the index α is omitted since it takes
only one value.
© 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
371
Conventions
This book uses natural units where c = ¯
h = 1, but the string length s (or Regge
slope α ) is kept.
A bar is used to denote both the complex conjugation and the anti-holomorphic
operators. The symbol := (resp,. =:) means that the LHS (RHS) is defined by the
expression in the RHS (LHS).
A.1
Coordinates
The number of spacetime (target-space) dimensions is denoted by D = d +1, where
d is the number of spatial dimensions. The corresponding spacetime and spatial
coordinates are written with Greek and Latin indices:
x
μ
= (x
0 , x
i ),
μ = 0, . . . , D − 1 = d
i = 1, . . . , d.
(A.1)
When time is singled out, one writes x 0 = t in Lorentzian signature and x 0 = t E
in Euclidean signature (or x 0 = τ when there is no ambiguity with the worldsheet
time).
A p-brane is a (p + 1)-dimensional object whose worldvolume is parametrized
by coordinates:
σ
a
= (σ
0 , σ
α ),
a = 0, . . . , p − 1,
α = 1, . . . , p.
(A.2)
The time coordinate can also be singled out as σ 0 = τ M in Lorentzian signature and
σ 0 = τ in Euclidean signature. For the string, the index α is omitted since it takes
only one value.
© 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
371