## Spiky strings and the AdS/CFT correspondence

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##### Authors

Losi, Manuel

##### Advisors

Dorey, Nicholas

##### Date

2011-10-11##### Awarding Institution

University of Cambridge

##### Author Affiliation

Department of Applied Mathematics and Theoretical Physics

##### Qualification

Doctor of Philosophy (PhD)

##### Language

English

##### Type

Thesis

##### Metadata

Show full item record##### Citation

Losi, M. (2011). Spiky strings and the AdS/CFT correspondence (Doctoral thesis). https://doi.org/10.17863/CAM.16106

##### Abstract

In this dissertation, we explore some aspects of semiclassical type IIB string
theory on AdS3 × S1 and on pure AdS3 in the limit of large angular momentum
S.
We first focus on the integrability technique known as finite-gap formalism
for strings in AdS3 × S1, leading to the definition of a hyperelliptic Riemann
surface, the spectral curve, which encodes, albeit in a rather implicit fashion,
the semiclassical spectrum of a very large family of string solutions. Then, we
show that, in the large angular momentum limit, the spectral curve separates
into two distinct surfaces, allowing the derivation of an explicit expression for
the spectrum, which is correspondingly characterised by two separate branches.
The latter may be interpreted in terms of two kinds of spikes appearing on the
strings: “large” spikes, yielding an infinite contribution to the energy and angular
momentum of the string, and “small” spikes, representing finite excitations over
the background of the “large” spikes.
According to the AdS/CFT correspondence, strings moving in AdS3 × S1
should be dual to single trace operators in the sl(2) sector of N = 4 super Yang-
Mills theory. The corresponding one-loop spectrum in perturbation theory may
also be computed through integrability methods and, in the large conformal spin
limit S → ∞ (equivalent to the AdS3 angular momentum in string theory) is
also expressed in terms of a spectral curve and characterised in terms of the
so-called holes. We show that, with the appropriate identifications and with
the usual extrapolation from weak to strong ’t Hooft coupling described by the
cusp anomalous dimension, the large-S spectra of gauge theory and of string
theory coincide. Furthermore, we explain how “small” and “large” holes may be
identified with “small” and “large” spikes.
Finally, we discuss several explicit spiky string solutions in AdS3 which, at
the leading semiclassical order, display the previously studied finite-gap spectrum.
We compute the spectral curves of these strings in the large S limit, finding that
they correspond to specific regions of the moduli space of the finite-gap curves.
We also explain how “large” spikes may be used in order to extract a discrete
system of degrees of freedom from string theory, which can then be matched with
the degrees of freedom of the dual gauge theory operators, and how “small” spikes
are in fact very similar to the Giant Magnons living in R × S2.

##### Keywords

String theory, AdS/CFT

##### Sponsorship

Domestic Research Scholarship (fees only); Cambridge European Trust and Isaac Newton Trust (Isaac Newton Trust European Research Studentship).