Spinning pulsating strings in $$(AdS_5 \times S^5)_{\varkappa }$$

The European Physical Journal C, Apr 2018

We study a general class of spinning pulsating strings in \((AdS_5 \times S^5)_{\varkappa }\) background. For these family of solitons, we examine the scaling relation between the energy, spin or angular momentum. We verify that in \(\varkappa \rightarrow 0 \) limit these relations reduce to the undeformed \(AdS_5 \times S^5\) case. We further study an example of a string which is spinning in the \(\varkappa \)-deformed \({\hbox {AdS}}_5\) and \({\hbox {S}}^5\) simultaneously and find out the scaling relation among various conserved charges.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-018-5749-5.pdf

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)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-018-5749-5.pdf

Sorna Prava Barik, Kamal L. Panigrahi, Manoranjan Samal. Spinning pulsating strings in $$(AdS_5 \times S^5)_{\varkappa }$$, The European Physical Journal C, 2018, pp. 280, Volume 78, Issue 4, DOI: 10.1140/epjc/s10052-018-5749-5