Spinning pulsating strings in $$(AdS_5 \times S^5)_{\varkappa }$$
Eur. Phys. J. C
Spinning pulsating strings in ( Ad S5 × S5)
Sorna Prava Barik 0
Kamal L. Panigrahi 0
Manoranjan Samal 0
0 Department of Physics, Indian Institute of Technology Kharagpur , Kharagpur 721 302 , India
We study a general class of spinning pulsating strings in ( Ad S5 × S5) background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in → 0 limit these relations reduce to the undeformed Ad S5 × S5 case. We further study an example of a string which is spinning in the -deformed AdS5 and S5 simultaneously and find out the scaling relation among various conserved charges.
1 Introduction
The AdS/CFT correspondence relates string states on AdS
and gauge invariant operators in the gauge theory side. The
most studied example of the AdS/CFT duality is the one
between spectrum of closed superstrings (supergravity) in
Ad S5 × S5 background and gauge invariant operators in four
dimensional N = 4 Supersymmetric Yang–Mills (SYM)
theory based on the gauge group SU (N ) [
1–3
]. A remarkable
feature of AdS/CFT duality is an underlying integrability
[
4
] structure on both side, which provides an important tool
for finding the spectrum on both sides and many significant
properties have been revealed based on exact computations.
To understand the structure of full string spectrum, one need
to identify the classical solitonic solutions of Ad S5 × S5
sigma model carrying global charges. The Yang–Mills theory
itself can be mapped to a integrable spin-chain system [
5
].
The basic idea of relating all string states to precise dual
gauge theory operators is a tough job due to presence of
infinite tower of string solutions on string theory side. One
probable way out of this problem is that in the large angular
momentum or large R-charge limit both sides of the duality
become more tractable. One of the advantages of this limit is
that the anomalous dimension of operators in the SYM theory
can be related to the dispersion relation between conserved
charges of spinnings and pulsating strings in the large charge
limit.
In this context, a large variety of rotating and spinning
strings has been studied in Ad S5 × S5 precisely and also have
been mapped to dual spin-chain excitations. These include
the already well studied giant magnon, folded strings and
spiky strings solutions and the gauge theory duals have been
analyzed in great detail. In spinning string case the highly
excited string states corresponds to the gauge theory
operators with small anomalous dimension. This type of strings is
the generalization of the folded [
6,7
] and spiky [8] strings
with single spin in AdS3 part of AdS5. The semiclassical
multi spinning string states (strings spinning in AdS5) have
also been found to be dual to certain trace operators [
9
]. It
has been shown that for these solutions, the string states are
unstable for large charges [
10
]. On the other hand, the circular
pulsating string solutions have been less explored. Pulsating
strings were first introduced in [
11
] where they were expected
to correspond to certain highly excited sigma model
operators and later on were generalized to [
12–14
]. In [
11
] and
[
15
], pulsating string solutions in Ad S5 and S5 respectively
have been worked out separately where as in [
16
], a string
rotating and at the same time oscillating in Ad S5 have been
derived. It has been shown that the addition of oscillation
to spinning strings improve the stability of the string states
[
17
]. An interesting class of solutions were proposed in [
18
]
which generalized some of the earlier pulsating and
spinning string solutions by looking at strings which are straight
and spinning in one direction but circular and pulsating in
another, and with a non-trivial coupling between the two in
Ad S5 × S5 background. Even though the exact gauge
theory operators corresponding to these class of string states are
still unknown, they are interesting in their own right. In this
paper, we wish to generalize such spinning pulsating strings
in ( Ad S5 × S5) background, the sigma model associated to
which retains integrability of the original model.
To explore the integrability beyond the usual Ad S5 × S5,
it is natural to consider the integrable deformation of the
background to study the string motion as well as the
underlying gauge theory, if any. Following the earlier proposals
about Yang–Baxter deformation made in [
19–21
], a
oneparameter deformed Ad S5 × S5 supercoset model was
constructed in [
22–24
]. The background string metric and the
NS–NS 2-form corresponding to deformed structure has been
worked out [
25
]. The symmetry group S O(2, 4) × S O(6) of
Ad S5 × S5 reduced to its Cartan subgroup [U (1)]6 and it
produced a nice laboratory to study string motion. Given the
integrable nature of the deformed background, various rigidly
rotating and pulsating strings have been investigated in detail
[
26–31
] (...truncated)