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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.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

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/

SCOAP

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