Physics Letters B 795 (2019) 225–229
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Probing tachyon kink s in Newton-Cartan background
Dibakar Roychowdhury
Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India
a r t i c l e i n f o a b s t r a c t
Article history:
Received
7 April 2019
Received
in revised form 13 June 2019
Accepted
14 June 2019
Available
online 17 June 2019
Editor:
N. Lambert
In this paper, we perform a systematic analysis of tachyon condensation over string Newton-Cartan (NC)
geometry by probing the background with non BPS Dp brane. We construct the finite tachyon effective
action for NC geometry and explore the dynamics associated with the tachyon kink on the world-volume
of the non BPS Dp brane. We show that under certain specific assumptions, the spatial dependent
tachyon condensation leads to an emerging BPS D(p − 1) brane dynamics over NC background. We
further compute the stress energy tensor and show the equivalence between two different Dp brane
configurations in the NC limit.
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Overview and motivation
Over the last couple of decades, the non relativistic string the-
ory
[1]with world-sheet Galilean invariance has attained renewed
attention due to its several remarkable features. One of the major
aspects associated with the non relativistic formulation of string
theory turns out to be the existence of an UV finite unitary de-
scription
that governs the stringy dynamics over a Galilean in-
variant
geometry [2–11]. Interestingly enough, the non relativistic
string spectrum does not seem to contain any massless excitation
which therefore sort of guarantees that the corresponding low en-
ergy
dynamics associated with that of the target space geometry
is not governed by Einstein gravity. On contrary, the correspond-
ing
target space geometry turns out to be string Newton-Cartan
(NC) background [12–16] which differs significantly from that of
the usual Riemannian spacetime.
Recently,
there has been a lot of attention towards a profound
understanding of stringy dynamics over NC background [17,18].
For example, a systematic theoretical formulation of four dimen-
sional
extended string Newton-Cartan gravity has been provided
by authors in [17]. However, in spite of these attem pts, several
crucial issues associated to string NC geometry are yet to be an-
swered.
One fundamental question that remains to be addressed is
the understanding of the dynamics of tachyon kinks [19–26]on the
world-volume of non BPS Dp branes [27–29] embedded in NC ge-
ometry.
The purpose of the present article is therefore twofold- (i)
to construct an effective field theory for tachy ons in the NC limit
[16] and (ii) to check whether the kink solution associated with
E-mail addresses: dibakarphys@gmail.com, dibakarfph@iitr.ac.in.
non BPS Dp branes can give rise to an emerging D(p − 1) brane
dynamics over string NC geometry.
Our
analysis reveals that tachy on condensation over string NC
geometry differs significantly from that of the earlier analysis in
several aspects. First of all, in order to have a finite world-volume
theory for non BPS Dp branes one needs to consider the effective
WZ coupling to be different from that of the usual coupling as-
sociated
with the DBI action. More specifically, we show that in
order for the action to be finite this WZ coupling has to go linearly
with
the NC parameter (ω) in the limit ω →∞. Secondly, unlike
the previous analysis [19], one needs to consider the most generic
ansatz
for the scalar modes living on the world-volume of non BPS
Dp brane. We show that a systematic analysis of the kink solu-
tion
(subjected to a set of constraints) performed under these two
assumptions naturally leads towards an emerging D(p − 1) brane
dynamics in the NC (ω →∞) limit [16]. In order to solidify our
claim, we further compute the stress energy tensor(s) associated
with the non BPS Dp brane configuration and show that it is ex-
actly
equal to the stress energy tensor(s) associated with the BPS
D(p −1) brane dynamics once the tachyon equation of motion to-
gether
with the above set of constraints are taken care of.
The
rest of the paper is organized as follows. We start with a
formal construction of effective field theory for tachyons in Sec-
tion 2.
In Section 3, we explore the dynamics associated with
tachyon kinks (over string NC geometry) and show that this dy-
namics
is equivalent to that of the BPS D(p − 1) dynamics once
a certain set of constraints together with the tachyon equation of
motion are imposed. To complete this analogy, we further com-
pute
stress tensor(s) in Section 4 and show that these two brane
configurations are equivalent. Finally, we conclude in Section 5.
https://doi.org/10.1016/j.physletb.2019.06.031
0370-2693/
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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