LARGE WINDING SECTOR OF AdS/CFT

Abstract

We study a family of classical strings on R × S 3 subspace of the AdS 5 × S 5 background that interpolates between pulsating strings and single-spike strings. They are obtained from the helical strings of hep-th/0609026 by interchanging worldsheet time and space coordinates, which maps rotating/spinning string states with large spins to oscillating states with large winding numbers. From a finite-gap perspective, this transformation is realised as an interchange of quasi-momentum and quasi-energy defined for the algebraic curve. The gauge theory duals are also discussed, and are identified with operators in the non-holomorphic sector of N = 4 super Yang-Mills. They can be viewed as excited states above the "antiferromagnetic" state, which is "the farthest from BPS" in the spin-chain spectrum. Furthermore, we investigate helical strings on AdS 3 × S 1 in an appendix.

Semiclassical SL(2) strings on LLM backgrounds

“…At first glance there is a rescaling of the coupling as λ → r 2 0 (1 +V φ (∞))λ. However, this is exactly the dispersion relation in the appendix of [45] with no rescaling. The way to see this is to realise that r 2 0 (1+V φ (∞)) sums the area of all the black regions on the LLM plane -this is a fixed quantity for all LLM geometries!…”

“…It is for this reason that we would like to study the SL(2) sector of nonplanar N = 4 SYM on an LLM geometry. Our primary focus is on the string theory side of the correspondence, where we may compare with several works in the planar limit such as [40][41][42][43][44][45] and see if the rescaled coupling proposal of [21] is manifest in the spectrum of strings dual to localised operators. We hope furthermore to gain some insight into how the subsectors may be isolated on the string theory side.…”

The omega-infinity limit of single spikes

“…7 The direct analogs of giant magnons for the AF ground state are single spikes (SSs) [23,24]. These are the string theory duals of N = 4 SYM (single) spinon states [25],…”

“…Like giant magnons, single spikes also belong to the class of long strings/strongly coupled operators for which there are no advanced spectroscopic tools at our disposal. Single spikes can be transformed to giant magnons by means of the τ ↔ σ transform or "2D duality" [25]:…”

Semiclassical strings on curved branes

“…Further, it was observed that N = 4 SYM in planar limit can be described by an integrable spin chain model where the anomalous dimension of the gauge invariant operators were found in [6], [7], [8], [9], [10], [11], [12]. In the dual picture, it was noticed that the string theory is integrable in the semiclassical limit as well, see for example [13], [14], [15], [16], [17], hence providing further insight into the AdS/CFT duality. However apart from few 'solvable' examples of AdS/CFT, in many cases the exact nature of the boundary operators is not known, and hence it is interesting to make calculations in the gravity side and then look for possible operators on the boundary by invoking the duality map.…”