Physics Letters B 773 (2017) 142–149
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Physics Letters B
www.elsevier.com/locate/physletb
Glueball–baryon interactions in holographic QCD
Si-Wen Li
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, Anhui, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
9 March 2017
Received
in revised form 10 July 2017
Accepted
10 August 2017
Available
online 18 August 2017
Editor:
M. Cveti
ˇ
c
Studying the Witten–Sakai–Sugimoto model with type IIA string theory, we find the glueball–baryon
interaction is predicted in this model. The glueball is identified as the 11D gravitational waves or
graviton described by the M5-brane supergravity solution. Employing the relation of M-theory and type
IIA string theory, glueball is also 10D gravitational perturbations which are the excited modes by close
strings in the bulk of this model. On the other hand, baryon is identified as a D4-brane wrapped
on S
4
which is named as baryon vertex, so the glueball–baryon interaction is nothing but the close
string/baryon vertex interaction in this model. Since the baryon vertex could be equivalently treated as
the instanton configurations on the flavor brane, we identify the glueball–baryon interaction as “graviton–
instanton”
interaction in order to describe it quantitatively by the quantum mechanical system for the
collective modes of baryons. So the effective Hamiltonian can be obtained by considering the gravitational
perturbations in the flavor brane action. With this Hamiltonian, the amplitudes and the selection rules of
the glueball–baryon interaction can be analytically calculated in the strong coupling limit. We show our
calculations explicitly in two characteristic situations which are “scalar and tensor glueball interacting
with baryons”. Although there is a long way to go, our work provides a holographic way to understand
the interactions of baryons in hadronic physics and nuclear physics by the underlying string theory.
© 2017 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. Introduction
The underlying fundamental theory QCD for nuclear physics
and particle physics has achieved great successes. However, nu-
clear
physics remains one of the most difficult and intriguing
branches of high energy physics because physicists are still un-
able
to analytically predict the behavior of nuclei or even a sin-
gle
proton. The key problem is that the behavior in the strong-
coupling
regime of QCD is less clear theoretically. Fortunately,
gauge/gravity (gauge/string) duality (see, e.g., [1–5] for a review)
has become a revolutionary and powerful tool for studying the
strongly coupled quantum field theory. Particularly, the Witten–
Sakai–Sugimoto
(WSS) model [6–8], as one of the most famous
models, has been proposed to holographically study the non-
perturbative
QCD for a long time [9–19]. Therefore, in this paper,
we are going to extend the previous works to study the interac-
tions
in holographic QCD.
The
holographic glueball–meson interaction has been studied in
[20–23] by naturally considering the gravitational waves or gravi-
ton
in the bulk of this model. Since the gravitational waves or
graviton signals the glueball states holographically and mesons are
E-mail address: cloudk@mail.ustc.edu.cn.
excited by the open string on the flavor branes, the close/open
string (on the flavor brane) interaction is definitely interpreted as
glueball–meson interaction. And the effective action could be de-
rived
by taking account of the gravitational perturbation in the
flavor brane action.
On
the other hand, in the WSS model, baryon could be identi-
fied
as a D4
-brane
1
wrapped on S
4
, which is named as “baryon
vertex” [24,25]. The D4
-brane has to attach the ends of N
c
fun-
damental
strings since the S
4
is supported by N
c
units of a R–R
flux in the supergravity (SUGRA) solution. Such a D4
-brane is
realized as a small instanton configuration in the world-volume
theory of the flavor branes in this model. Basically, the baryon
states could be obtained by quantizing the baryon vertex. In the
strong coupling limit (i.e. the t’ Hooft coupling constant λ 1),
the two-flavor case (i.e. N
f
= 2) has been studied in [9] and it
turns out that baryons can be described by the SU(2) Belavin–
Polyakov–Schwarz–Tyupkin
(BPST) instanton solution with a U
(
1
)
potential in the world-volume theory of the flavor branes. And em-
ploying
the soliton picture, baryon states could be obtained by a
1
In order to distinguish from N
c
D4-branes who are responsible for the back-
ground
geometry, we denote the baryon vertex as “D4
-brane” in this paper.
http://dx.doi.org/10.1016/j.physletb.2017.08.011
0370-2693/
© 2017 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
.