Physics Letters B 751 (2015) 352–357
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Radiation Gauge in AdS/QCD: Inadmissibility and implications on
spectral functions in the deconfined phase
David Dudal
a,b,∗
, Thomas G. Mertens
b,c
a
KU Leuven Campus Kortrijk – KULAK, Department of Physics, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium
b
Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium
c
Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
20 October 2015
Accepted
26 October 2015
Available
online 30 October 2015
Editor:
M. Cveti
ˇ
c
We point out a subtlety in choosing the radiation gauge (A
z
= 0combined with the Lorenz gauge) for
gauge fields in AdS/QCD for black hole backgrounds. We then demonstrate the effect of this on the
momentum-dependence of the spectral functions of the J/ψ vector meson, showing a spreading with
momentum and a breaking of isotropy, in contrast to previous results in the literature. We also discuss
the dependence on a background magnetic field, following our earlier proposed model.
© 2015 The Authors. 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
In this note, we would like to discuss in detail the choice of
the radiation gauge as it is frequently applied in holographic ap-
proaches
to QCD. Our specific interest arose from the soft wall
model, but the arguments given in the next section do apply to
any gauge field in an AdS or AdS black hole background.
In
the soft wall model, one studies excitations of a gauge field
in AdS with action
S =−
1
4g
2
5
d
5
x
√
−ge
−
tr
F
L,MN
F
L,MN
+ F
R,MN
F
R,MN
,
(1)
for left and right gauge fields A
L
and A
R
. We will denote
5-dimensional indices as M, N, O , P and 4-dimensional (bound-
ary)
indices with μ, ν. The corresponding equations of motion of
either gauge field are given by:
∂
M
e
−
√
−GG
MO
G
NP
(∂
O
A
P
−∂
P
A
O
)
=0, (2)
where the background geometry is either AdS:
ds
2
=
L
2
z
2
−
dt
2
+dx
2
+dz
2
,
e
−
=e
−cz
2
, (3)
or the AdS black hole:
*
Corresponding author at: KU Leuven Campus Kortrijk – KULAK, Department of
Physics, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium.
E-mail
addresses: david.dudal@kuleuven-kulak.be (D. Dudal),
tmertens@princeton.edu (T.G. Mertens).
ds
2
=
L
2
z
2
−
f (z)dt
2
+dx
2
+
dz
2
f (z)
,
e
−
=e
−cz
2
, (4)
with f (z) = 1 − z
4
/z
4
h
and z = z
h
the horizon location. The back-
ground
includes a dilaton field whose backreaction on the ge-
ometry
is assumed to be minor. This model gained popularity to
holographically capture important QCD physics, e.g. because of its
correct scaling behavior of the meson spectrum and the reader
is referred to elsewhere for more motivation and details of this
model [1–3].
As
a particular example where the soft model was used to
study strongly coupled QCD physics, let us refer to [4,5] where
heavy quarkonia were studied. The authors of [4,5] suggested
choosing a flavor-dependent soft-wall parameter c, where the light
quarks (u, d, s) are combined into a SU(3)
L
× SU(3)
R
soft wall
model and the heavy quark of interest (charm in our case) is
treated on its own in a U (1)
L
×U (1)
R
Abelian model:
S =−
d
5
x
√
−g tr e
−c
ρ
z
2
L
light
+e
−c
J /ψ
z
2
L
charm
. (5)
Our goal in this work is to compute the momentum-depen-
dence
of the
¯
cc spectral function in this model and to demonstrate
that one of the conclusions of [4,5], namely that isotropy (rota-
tional
invariance) is present in the spectral function, is actually a
consequence of a forbidden choice of gauge.
2. Survey of the radiation gauge in AdS/CFT
The field A
μ
has of course a large gauge redundancy and we
will investigate here whether the radiation gauge can always be
http://dx.doi.org/10.1016/j.physletb.2015.10.074
0370-2693/
© 2015 The Authors. 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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