Multi-spin string solutions in AdS black hole and confining backgrounds

Abstract

We study semi-classical multi-spin strings in the non-supersymmetric backgrounds of AdS Black Hole and Witten's confining model. We consider constant radius strings with rotations along the isometries of the backgrounds. In the AdS Black Hole, solutions exist only if there is a non-zero spin in the Black Hole part. In contrast with the AdS background, we find solutions which although have no rotation in the S 5 part, have a regular λ expansion in the expression for large energy. In the near-extremal D 3 and D 4 backgrounds, we find that strings have to be located on the confining wall. We also discuss the stability of solutions by considering the fluctuation Lagrangians.1 Alishah@theory.ipm.ac.ir 2 Mosaffa@theory.ipm.ac.ir 3 yavar@theory.ipm.ac.irChecking AdS/CFT conjecture [1] received a major boost after the plane-wave (BMN) limit of the AdS 5 × S 5 background was introduced [2]. The idea in the BMN limit was that for a certain subset of string states which are parameterized by large quantum numbers there exist limits in which quantum corrections coming from the string sigma model are suppressed beyond the second order. Shortly afterwards, the BMN limit was understood by a new approach based on semi-classical analysis of strings [3] which gave way to understanding more general cases. The approach was based on considering classical configurations of strings having different charges such as angular momentum along the isometries of the AdS 5 × S 5 and then expanding the string sigma model around the configuration. The BMN limit was reproduced in the limit where the string shrinks to a point and moves with a large angular momentum J along a large circle of S 5 . A considerable amount of work followed in this line [4]- [26].A key observation in this approach was that by turning on more and more classical charges, the sigma model corrections are pushed to higher and higher orders which for large charges become more and more unimportant. Such multi-spin configurations were found in [27,28] for which the classical energy has a regular expansion in λ J 2 (where λ is the 't Hooft coupling and J is a typical charge) and the sigma model corrections are suppressed by powers of 1 J . This led to the proposal that for such states, the classical energy expanded in λ J 2 ≪ 1 could be compared to the corresponding quantum anomalous dimensions in perturbative SYM theory. The proposal was verified in a series of papers using the integrable model techniques on the SYM side [29]- [34]. The main observation in this direction was made in [35,36] where the authors have shown how to find the eigenvalues of anomalous dimension matrix for large J scalar operators by interpreting the anomalous dimension matrix as an integrable spin-chain Hamiltonian. For further study in this direction see [37]-[50].So far people have studied those cases in which the dual gauge theory is supersymmetric. Among the string configurations studied in these backgrounds, for which the classical energy has a regular expansion in λ, all share the property that the ...

Super Yang–Mills and the XXZ spin chain

“…computed from (24). In this sense, these operators are the analogous in the N = 2 theory of the BPS (or chiral primary) operators of the N = 4 SYM [31,32,33,34].…”

Semiclassical string spectrum in a string model dual to large N QCD

“…1 Previous discussions on semiclassical string solutions in this model are in [19,20]. Studies of semiclassical string solutions in other confining backgrounds can be found in [21].…”

“…The configuration 20) with ω, n, m > 0, solves the equations of motion and Virasoro constraints with (…”

LOGARITHMIC CORRECTION TO SCALING FOR MULTISPIN STRINGS IN THE AdS5 BLACK HOLE BACKGROUND

“…Notice that we get two solutions, as in the case where the string is not extended in the radial direction [21]. In our case we get from equations (39) and (40) …”

“…A one-spin string orbiting around the black hole was constructed in [20], leading in the long string and high temperature limit to a result similar to equation (1). A two-spin string was constructed in [21], but it was not extended in the radial direction and it did not lead to a relation similar to equation (2).…”