Physics Letters B 750 (2015) 379–383
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
On the regularization of extremal three-point functions involving giant
gravitons
Charlotte Kristjansen
a
, Stefano Mori
a
, Donovan Young
b,∗
a
Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
b
Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
a r t i c l e i n f o a b s t r a c t
Article history:
Received
22 July 2015
Accepted
22 September 2015
Available
online 28 September 2015
Editor:
N. Lambert
Keywords:
AdS/CFT
correspondence
Giant
gravitons
Three-point
functions
ABJM
theory
In the AdS
5
/CFT
4
set-up, extremal three-point functions involving two giant 1/2 BPS gravitons and
one point-like 1/2 BPS graviton, when calculated using semi-classical string theory methods, match
the corresponding three-point functions obtained in the tree-level gauge theory. The string theory
computation relies on a certain regularization procedure whose justification is based on the match
between gauge and string theory. We revisit the regularization procedure and reformulate it in a way
which allows a generalization to the ABJM set-up where three-point functions of 1/2 BPS operators are
not protected and where a match between tree-level gauge theory and semi-classical string theory is
hence not expected.
© 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
.
After the successful application of integrability techniques to
the planar spectral problem of the AdS
5
/CFT
4
set-up [1], the cal-
culation
of three-point functions in the same set-up has attracted
renewed attention with some recent highlights being the conjec-
ture
of an all loop formula for three-point functions of single trace
operators in certain sub-sectors of N = 4SYM [2] and the formu-
lation
of certain integrability axioms for the cubic string theory
vertex [3].
We
will be considering three-point functions which do not be-
long
to the class of three-point functions considered in the above
references. Our three-point functions involve giant gravitons which
in the string theory language cor respond to higher dimensional D-
or
M-branes wrapping certain submanifolds of the string theory
background and which in the gauge theory picture are represented
by specific linear combinations of multi-trace operators, namely
Schur polynomials. Remaining in the gauge theor y picture, our
three-point functions will involve two Schur polynomials and one
single trace operator, all of 1/2BPS type. Furthermore, the three
operators will be chosen such that
1
=
2
+
3
, where the ’s
are the conformal dimensions of the operators. Such three-point
functions are denoted as extremal three-point functions and are
known to require special care in the comparison between gauge
and string theory [4]. On the gauge theory side the three-point
functions of interest can be calculated using techniques from zero-
*
Corresponding author.
E-mail
addresses: kristjan@nbi.ku.dk (C. Kristjansen), moriste@nbi.ku.dk
(S. Mori),
d.young@qmul.ac.uk (D. Young).
dimensional field theories [5] (see also [6]) and on the string
theory side they can be determined by generalizing a method de-
veloped
for the calculation of heavy–heavy–light correlators [7–9]
from
string states to membranes [5].
In
the case of the AdS
5
× S
5
correspondence the 1/2-BPS na-
ture
of the operators involved implies that the three-point func-
tion
considered is protected and thus should take the same value
whether calculated in string theory or in gauge theory. As pointed
out in [10] the need for special treatment of extremal correlators
in string theory is relevant here and in [11] a regularization pro-
cedure
for the string theory computation which led to the desired
match between gauge and string theory was presented.
The
AdS
4
× CP
3
set-up [12] allows one to consider a simi-
lar
correlator i.e. an extremal three-point function involving two
1/2 BPS giant gravitons in combination with one 1/2 BPS point-
like
graviton and the methods developed in [5] for the AdS
5
/CFT
4
calculation can be generalized to this case as well [13]. One re-
maining
subtle point is the choice of regularization procedure in
the string theory computation. In the AdS
4
× CP
3
correspondence
three-point functions of 1/2 BPS operators are not protected and
hence in this set-up we cannot expect a match between gauge and
string theory results. In particular, this means that on one hand
we cannot justify our choice of regulator by a match between the
gauge and string theory results but on the other hand a compu-
tation
of the correlator in the weakly coupled string theory will
provide us with a non-trivial prediction about the behaviour of the
correlator in the dual strongly coupled field theory. Below we will
revisit the regularization procedure employe d for the AdS
5
× S
5
http://dx.doi.org/10.1016/j.physletb.2015.09.056
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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