Eur. Phys. J. C (2019) 79:81
https://doi.org/10.1140/epjc/s10052-019-6541-x
Regular Article - Theoretical Physics
Investigation of zero-modes for a dynamical D p-brane
Farzin Safarzadeh-Maleki
a
Amirkabir University of Technology, Tehran, Iran
Received: 1 August 2018 / Accepted: 3 January 2019 / Published online: 28 January 2019
© The Author(s) 2019
Abstract In this article, we investigate zero-modes for a
dynamical (rotating-moving) Dp-brane, coupled to the elec-
tromagnetic and tachyonic background fields. This work
is done by the boundary state methods, in three cases of
bosonic and fermionic boundary states and superstring parti-
tion function. By analyzing the obtained zero-modes in either
of the cases, interesting results will be obtained. Our findings
demonstrate the importance of the zero-mode and its effects
on the background fields and the defined internal properties
of the described system.
1 Introduction and conclusion
So far many significant aspects of D-branes [1,2], as an essen-
tial objects of string/superstring theory, have been discov-
ered. D-branes, interpreted as the classical solutions of the
low energy string effective action, could be defined in terms
of closed strings. Meanwhile, the boundary state method [3–
5], as a powerful technique, can be considered to show the
couplings of all closed string states to D-branes. Boundary
state method is a beneficial approach in many complicated
situations, even when a clear space-time is not accessible. By
applying the boundary state method for describing D-branes,
different properties and many configurations of these objects
have been studied [6–12]. Another description of D-branes,
as tachyonic solitons, follows from the boundary string field
theory, in which one can codify the information by using
the disc partition function of the open string sigma model.
In this context, for the case of superstring theory, an effec-
tive space-time action can be obtained by the corresponding
world-sheet partition function [13–19].
In most articles in which have been studied the issue of
the boundary state, the zero-modes have been neglected for
simplifying the calculation and hence, the zero-modes effects
have been omitted from the system. In this paper, we concen-
a
e-mail: f.safarzadeh@aut.ac.ir
trate specifically on the zero-modes and their effects on the
properties of the system under study, such as its dynamics
and background fields. This work is done by studying the
zero-modes boundary states, for both bosonic and fermionic
theory and also for zero-mode superstring partition function,
corresponding to a rotating-moving Dp-brane which is cou-
pled to a U (1) gauge potential in the world-volume of the
brane (photonic field) and tachyonic background field as open
string states.
By investigating the zero-modes in each case, interesting
results will be obtained. For example, according to the initial
condition and the theory (bosonic or fermionic) which is cho-
sen, the background fields contributions to the zero-modes
would be different. In the zero-mode bosonic boundary state,
photonic background field would be disappeared. The rea-
son behind that can be explained either by the boundary state
method or by the path integral techniques. The former is due
to the zero-mode boundary state equation, which is obtained
by substituting the zero-mode solution of the closed string
equation of motion into the boundary equations. It should
be noted that in the case of compact space-time this result
could be changed. However, in this paper we assume a non-
compact flat space-time and therefore in the bosonic theory,
the photonic term would be absent in the zero-mode bound-
ary state. On the other hand, for the fermionic theory, the
electromagnetic field would be present and existence of the
tachyon field could depend on the choice of the σ ’s value.
Moreover, we study the explicit form of the fermionic
zero-mode boundary state, for both type IIA and type IIB
theories, corresponding to the present rotating-moving Dp-
brane with tachyonic and photonic boundary action. By eval-
uating different configurations of the described system, i.e.,
omitting the background fields and/or rotating-moving struc-
ture, our system would overlap some familiar brane structures
in the literature. In continue, we have listed some branes
configurations and their corresponding zero-mode R-R sec-
tor solutions in a classified table. This table shows how the
brane properties would affect the R-R zero-mode solution.
123